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4 


THE BAYNE-SYLVESTER 
ARITHMETIC 


BY . A ,, ' 

STEPHEN F.'^BAYNE 

DISTRICT SUPERINTENDENT OF SCHOOLS 
CITY OF NEW YORK 

EMMA SYLVESTER 

PRINCIPAL, JUNIOR HIGH SCHOOL 
CITY OF NEW YORK 

RUTH T. FITZELL 

PRINCIPAL, ELEMENTARY SCHOOL 
CITY OF NEW YORK 



SEVENTH GRADE 



D. C. HEATH AND COMPANY 


BOSTON 

ATLANTA 


NEW YORK 
SAN FRANCISCO 
LONDON 


CHICAGO 

DALLAS 





Copyright, 1930, 

By D. C. Heath and Company 


3E0 



PRINTED IN U.S.A. 


JUL 21 i930 


©CU 25582 


INTRODUCTION 

The Bayne-Sylvester Arithmetics have been written with 
the distinct purposes (1) of so grading arithmetical difficulties 
as to make the approach to new processes simple, and (2) of so 
arranging the material as to offer means for self-diagnosis of 
weakness and immediate remedy. 

Scope. — The series is based on the most recent investigations 
in the field of number combinations and in problem solving. 
It frankly discards the theme of “arithmetic for arithmetic’s 
sake” and accepts as a proper objective “arithmetic for every¬ 
day use.” Recognizing that the life of the average person today 
is rarely concerned with large numbers, with many decimal 
places, with denominations of undue size, the authors have 
limited the work in these fields to practical numbers, to decimals 
of reasonable size, and to fractions common in business trans¬ 
actions. Nevertheless, they are aware of the informative and 
socializing values of arithmetic, and a number of topics which 
were formerly taught for the purpose of developing skill in 
computation are given for information only. Thus the right 
of the child to know these processes and phases of business 
life is acknowledged, but the child is no longer required to 
perform laborious computations that the adult seldom needs to 
use. 

Use of Problems. —^ New processes are developed through 
problems that are interesting to children and expressed in 
language that they can easily comprehend. In this way the 
value of the process which he is to master is impressed upon the 
child. Specific training in problem solving is provided through¬ 
out the series. Methods of solution are those that have been 

iii 


IV 


INTRODUCTION 


thoroughly tested and accepted, rather than those that appeal 
because of novelty. The problems are so arranged as to make 
the pupil recognize that there is essentially little difference 
between what have been termed “oral” and “written prob¬ 
lems. By introducing problems with the admonition “Use 
pencil when needed,” this unity of problem work is stressed. 

Test Drills. — The Test Drills represent the result of study 
over a period of several years. They offer to the child a means 
of diagnosing for himself his difficulty in any fundamental proc¬ 
ess, and supply him with abundant material for drill, not on 
the entire process, but on the specific step of the process in which 
he has failed. This material for drill is incorporated in the 
diagnostic test itself; there is no necessity to turn to some other 
portion of the text for remedial work. Each example is designed 
to test a particular step in a given mathematical process, and is 
divided into several similar parts. The teacher directs the class 
to do the part of each example that appears in the column headed 
A, or B, or C, etc. If a pupil makes a mistake in any example 
assigned, he must do the example again correctly and then do 
also the parts of the same example that appear in the other 
columns. Thus, if the teacher assigns Part C and the pupil 
makes an error in Example 3, he must not only do Part C of 
Example 3 correctly, but he must also do Parts A, B, D, etc. 

Individual Differences are specifically cared for by the Test 
Drills and by additional examples, many of which call for work 
beyond the grade limits. Such examples are indicated by as¬ 
terisks. The use of the graph, now a required form of mathe¬ 
matical training, is fully developed in this connection. 

Silent Reading in arithmetic textbooks as a part of the “work 
type” of reading is found in many new courses of study. This 
series offers definite correlative exercises. Problems without 
numbers, problems requiring the formulation of the question, 
and problems calling only for the indicated solution serve as 
valuable material for silent reading. 


INTRODUCTION 


V 


Tests. — Beginning with the books for the fourth grade, 
sample achievement tests are given in each volume. These 
will serve as type tests for use by teachers from time to time 
in getting a cross section of the work of the class. Satisfactory 
performance in these tests is a guaranty that the pupil has 
grasped the essentials of the work for the grade. 


CONTENTS 



Part 

I- 

- Review 


SECTION PAGE 

SECTION 

PAGE 

1 . 

Numeration and Notation 

1 

21 . 

Selling Goods .... 

25 

2 . 

Decimals. 

3 

22 . 

Addition. 

26 

3. 

The Roman Notation . 

5 

23. 

Harder Addition Combina¬ 


4. 

Practice Exercises on Re- 



tions That Occur in 



duction of Fractions 

6 


Multiplication 

27 

5. 

Review of Common Frac- 


24. 

Step-by-Step Test Drill — 



tions. 

7 


Addition of Integers 

28 

6 . 

Addition of Fractions . 

8 

25. 

Step-by-Step Test Drill — 


7. 

Practice in Adding Frac- 



Addition of Decimals . 

29 


tions. 

9 

26. 

Subtraction .... 

30 

8 . 

How to Use the Step-by- 


27. 

Step-by-Step Test Drill — 



Step Test Drills . 

10 


Subtraction .... 

31 

9. 

Step-by-Step Test Drill — 


28. 

Step-by-Step Test Drill — 



Addition of Fractions . 

11 


Subtraction of Decimals 

32 

10 . 

Subtraction of Fractions . 

12 

29. 

Problems from Geography 

33 

11 . 

Practice in Subtraction of 


30. 

Multiplication .... 

36 


Fractions .... 

13 

31. 

Drill on the Difficult Mul¬ 


12 . Step-by-Step Test Drill — 



tiplication Combinations 

38 


Subtraction of Fractions 

14 

32. 

Placing the Decimal Point 


13. 

Multiplication of Fractions 

15 


in Multiplication 

39 

14. 

Practice in Multiplication 


33. 

Problems in Multiplication 

40 


of Fractions .... 

16 

34. 

Step-by-Step Test Drill — 


15. Step-by-Step Test Drill — 



Multiplication of Deci¬ 



Multiplication of Frac¬ 



mals . 

41 


tions . 

17 

35. 

Division. 

42 

16. 

Division of Fractions . 

18 

36. 

Buying by the Hundred 


17. 

Practice in Division of 



and the Thousand . 

44 


Fractions .... 

19 

37. 

Review of Difficult Combi¬ 


18. Step-by-Step Test Drill — 



nations in Division . 

45 


Division of Fractions . 

20 

38. 

Selecting the Quotient . 

47 

19. 

Principles of Fractions Re¬ 


39. 

Step-by-Step Test Drill — 



viewed . 

21 


Division of Decimals 

48 

20 . 

Problems with Fractions . 

23 

40. 

Problems about Rainfall 

. 49 


VI 






CONTENTS 


Vll 


SECTION 

t>AGE 

SECTION 

PAGE 

41. Practice with Decimals . 

50 

57. 

Percentage Race 

73 

42. What You Should Know 


58. 

Step-by-Step Test Drill — 


about Decimals . 

51 


Percentage .... 

74 

43. Percentage. 

52 

59. 

Finding a Part of a Number 

75 

44. Finding a Per Cent of a 


60. 

Finding What Part One 


Number. 

53 


Number Is of Another . 

76 

45. Adding and Subtracting 


61. 

Problems. 

77 

Per Cents. 

56 

62. 

Finding a Number When a 


46. Per Cents More Than 100 

57 


Part Is Given 

78 

47. Short Ways of Finding Per 


63. 

Reduction of Denominate 


Cent. 

59 


Numbers. 

79 

48. Finding What Per Cent 


64. 

Liquid Measure 

81 

One Number Is of An- 


65. 

Linear Measure.... 

82 

other. 

61 

66. 

Measures of Time . 

83 

49. Problems in Percentage . 

63 

67. 

Square Measure 

84 

50. Finding a Number When a 


68. 

Measures of Weight 

85 

Per Cent Is Given . 

64 

69. 

Adding Denominate Num¬ 


51. Problem Review . 

66 


bers . 

86 

52. Completion Exercise . 

68 

70. 

Subtracting Denominate 


53. Per Cents Less Than One 



Numbers. 

87 

Per Cent. 

69 

71. 

Multiplying Denominate 


54. Sentences for Completion . 

70 


Numbers . . 

88 

55. Estimating. 

72 

72. 

Dividing Denominate 


56. Review of Percentage . 

72 


Numbers. 

89 

Part II — New Work 

OF 7A Grade 


73. Household Problems . 

90 

86. 

Finding Profit or Loss . 

118 

74. Paying for Electricity . 

“92 

87. 

Finding the Selling Price . 

119 

75. How to Read an Electric 


88. 

Finding the Per Cent of 


Meter. 

94 


Profit or Loss.... 

120 

76. Problems. 

95 

89. 

General Review of Profit 


77. Paying for Gas. 

97 


and Loss. 

122 

78. Problems. 

99 

90. 

Finding the Cost . 

124 

79. Thrift . 

100 

91. 

Commission . 

125 

80. Problems . 

102 

92. 

Finding the Net Proceeds 


81. Order Blanks .... 

105 


of a Sale. 

127 

82. Sales Slips. 

106 

93. 

A Short Way of Finding the 


83. Bills. 

109 


Net Cost. 

129 

84. Getting a Receipt . 

112 

94. 

Review of Terms in Com¬ 


85. Profit and Loss .... 

115 


mission . 

130 












viii CONTENTS 


SECTION 

PAGE 

SECTION 

PAGE 

95. 

Interest . 

131 

no. 

Silent Reading of Prob¬ 


96. 

Interest for One Year 

132 


lems . 

149 

97. 

Interest for More Than 


111. 

Our Ball Team . 

150 


One Year .... 

132 

112. 

Problems. 

151 

98. 

Interest for Less Than 


113. 

Studying a Time-Table . 

152 


One Year .... 

134 

114. 

Traveling by Airplane . 

153 

99. 

Interest for Years and 


115. 

Problems on Airplane 



Months. 

135 


Travel. 

155 

100. 

General Problems in In¬ 


116. 

Using a Ticket Schedule . 

156 


terest . 

137 

117. 

Parcel Post .... 

157 

101. 

Formula for Computing 


118. 

How to Send Money . 

160 


Interest . 

138 

119. 

Problems. 

161 

102. Step-by-Step Test Drill 


120. 

Right Angles and Rec¬ 



— Application of Per¬ 



tangles . 

161 


centage. I . . 

140 

121. 

Area of a Right Triangle. 

163 

103. Step-by-Step Test Drill 


122. 

Keeping a Record of Prog¬ 



— Application of Per¬ 



ress . 

164 


centage. II. . . . 

141 

123. 

Using the Bar Graph in 


104. Problem Analysis 

142 


Geography .... 

166 

105. 

Supplying the Question . 

144 

124. 

Standard Weights of a 


106. 

Approximating Answers . 

145 


Bushel. 

169 

107. 

Selecting the Operation . 

146 

125. 

Denominate Number 


108. 

Changing the Wording of 



Race. 

170 


Problems .... 

147 

126. 

Recording Your Progress 


109. 

Problems without Num¬ 



in Arithmetic . 

171 


bers . 

148 

127. 

Tests I-X. 

172 


Part III — New Work 

OF 7B Grade 


128. 

Problems. 

182 

136. 

The Interest Formula . 

200 

129. 

Practicing Thrift . 

186 

137. 

Compound Interest . 

201 

130. 

Discount Sales 

187 

138. 

Problems. 

203 

131. 

Finding the Net Cost . 

188 

139. 

Banks . 

204 

132. 

Trade or Commercial Dis¬ 


140. 

Paying Bills by Check 

206 


count—Successive Dis¬ 


141. 

Keeping an Account at 



counts . 

190 


the Bank .... 

210 

133. 

Interest — Review 

193 

142. 

Finding Interest from a 


134. 

Interest for 30, 60, 90, 



Graph . 

210 


Days—the 6% Method 

194 

143. 

Problems in Interest . 

213 

135. 

General Problems in In¬ 


144. 

Compound Interest . 

214 


terest . 

199 

145. 

Problems in Percentage . 

214 




CONTENTS 


IX 


SECTION 

146. Problems in Commission 

147. Miscellaneous Problems . 

148. Step-by-Step Test Drill 

— Application of Per¬ 
centage. I . . . . 

149. Step-by-Step Test Drill 

— Application of Per¬ 
centage. II. . . . 

150. Same — Different Test . 

151. Completing Sentences 

152. Foreign Money 

153. Problems . 

154. Taxes . 

155. Problems . 

156. United States Govern¬ 

ment Taxes — Customs 
and Duties .... 

157. Using Graphs for Com¬ 

parisons .... 

158. Problem Analysis . .. . 

159. Supplying the Question . 

160. Approximating Answers . 


SECTION PAGE 

161. Selecting the Operation . 236 

162. Changing the Wording of 

Problems .... 237 

163. Problems without Num¬ 

bers . 238 

164. Silent Reading of Prob¬ 

lems . 239 

165. Contents of Rectangular 

Solids . 241 

166. Cubic Measure . . . 245 

167. Problems.246 

168. Denominate Number Race 248 

169. A Holiday in the South . 249 

170. Commuting .... 252 

171. Reading a Time-Table . 254 

172. Showing the Results of a 

Competition . . . 255 

173. Vocabulary Test . . . 256 

174. Recording Your Progress 

in Arithmetic . . . 258 

175. Tests I-X . 259 

176. Tables of Measure . . 269 


PAGE 

216 

217 

220 

221 

222 

223 

224 

226 

227 

229 

230 

231 

232 

234 

235 

















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• iiJ' ■ V ■ 







THE BAYNE-SYLVESTER ARITHMETIC 







SEVENTH GRADE-PART I 


1. Numeration and Notation 

Numeration is the reading of numbers; notation is the 
writing of numbers. 

Numbers may be written in several ways: 

1. In words, as: five, seventeen. 

2. In the Arabic notation, as: 5, 17. 

3. In the Roman notation, as: V, XVII. 

The Arabic notation derives its name from the Arabs, 
who introduced it into Europe. It is a decimal system, 
based on groups of tens. The value of each order is ten 
times as great as the value of the next order to the right. 


Billions’ 

Period 

Millions’ 

Period 

Thousands’ 

Period 

Units’ 

Period 

Hundred Billions 

Ten Billions 

Billions 

Hundred Millions 

Ten Millions 

Millions 

Hundred Thousands 

Ten Thousands 

Thousands 

Hundreds 

Tens 

Units 

75, 308, 756, 205 


We read this number as follows: seventy-five billion, 
three hundred eight million, seven hundred fifty-six thousand, 
two hundred five. 









2 


THE BAYNE-SYLVESTER ARITHMETIC 


The numbers are pointed off into periods so that they 

may be more easily read. Each period consists of- 

orders. 

1. Read these numbers, which give the altitudes and 
areas of some of the African lakes: 


Altitude {Height 

Lake above Sea Level) Area 

Victoria . . ^. . . . 3700 ft. 26,800 sq. mi. 

Tanganyika. 2500 ft. 12,300 sq. mi. 

Nyassa. 1600 ft. 10,300 sq. mi. 

Chad. 850 ft. 10,000 sq. mi. 


2. Which lake is highest above sea level? Which is 
next highest? Which lake is largest in area? Which is 
smallest? 


3. Read the following: 


Continent 

Area 


North America .... 

. . . 9,031,000 

sq. 

mi. 

South America .... 

. . . 6,856,000 

sq. 

mi. 

Europe. 

. . . 3,842,000 

sq. 

mi. 

Asia. 

. . . 17,512,000 

sq. 

mi. 

Africa. 

. . . 11,510,000 

sq. 

mi. 

Australia. 

. . . 3,455,000 

sq. 

mi. 


4. Rewrite this list, placing the continents in order 
according to area, beginning with the smallest. 

5. The area of North America is about - that of 

Asia. 

6. The area of Asia is about_times as great as that 

of Australia. 











SEVENTH GRADE 


3 


2. Decimals 

In your work in arithmetic you will use decimals 
frequently. It is important, therefore, that you know 
how to use them. 

A decimal is a fraction. Its denominator is 10 or some 
power of 10. A power of a number is the number multi¬ 
plied by itself. For example, 100 is a power of 10 because 
it is equal to 10 X 10; similarly, 1000 is a power of 10 
because it is equal to 10 X 10 X 10. The understood 
denominator of a decimal, therefore, is 10, 100, 1000, 
10,000, 100,000. 

In writing a common fraction, both terms are expressed, 
tw- writing a decimal fraction, only the 
numerator is expressed. The denominator is understood, 
and is determined by the number of decimal places. A 
decimal fraction takes its name from its understood 
denominator. 

~ 10 0 ~ 10^00 ~ .007 to.Jcto “ .0007 

The period used in decimals is called the decimal 'point, 

1. Complete these statements: 

(a) A fraction with an unexpressed _ which is 10 

or some power of 10 is called a_fraction. 

ih) In a decimal fraction only the_is expressed. 

(c) The decimal fraction takes its name from the_ 

which is_ 

(d) The period used in a decimal fraction is called the 

(e) The denominator of a decimal fraction is deter¬ 
mined by the_of- 




4 


THE BAYNE-SYLVESTER ARITHMETIC 



2. Read: .034 .0034 .00034 

The following are mixed decimals: 

75.84 70.084 700.584 

A zero is often placed before a decimal point to call 
attention to it: 

0.07 0.75 0.5 0.13 

Zeros may be annexed to a decimal without changing 
its value: 

.6 = .60 .08 = .080 

3. Which pairs of numbers in the list below have the 
same values? 


(«) 

.5 

.50 

(d) 

5 

50 

(6) 

.01 

.1 

(e) 

.6 

6 

1 0 

(c) 

.07 

7 

T(T 

(/) 

.75 

3 

4 


4. Read the following statements: 

(а) A grain elevator contains 3749.55 bu, of wheat. 

(б) An automobile map gives the following information 
concerning the distance between certain places: Boston to 
Springfield, 94.7 mi.; Springfield to Pittsfield, 56.0 mi. 


















SEVENTH GRADE 


5 


3. The Roman Notation 

The Roman system of notation above 12 is used chiefly 
for (1) numbering the chapters of books; (2) numbering 
the voliunes in a series of books, as in the case of encyclo¬ 
pedias; (3) expressing dates in their formal use, as on 
momunents and on the cornerstones of buildings. 

In the Roman system the following seven letters, which 
are always capital letters, are used: 

I V X L C D M 

1 5 10 50 100 500 1000 

Complete the following statements: 

1 . When a letter is repeated, its value is_. 

1 = 1 X = 10 C = ? 

II = ? XXX = ? CC = ? 

2. When a letter of smaller value precedes a letter of 

greater value, the value of the smaller is-the 

value of the larger. 

Apply the rule in these examples: 

V=? X=? L=? C=? 

IV = ? IX = ? XL = ? XC = ? 

3. When a letter of smaller value follows a letter of 

greater value, the value of the smaller is_the 

value of the larger. 

Apply the rule in these examples: 

V=? X=? L=? C=? 

VI = ? XIII = ? " LX = ? CX = ? 

VIII = ? XVI = ? LXXIX = ? CXLVI = ? 



6 


THE BAYNE-SYLVESTER ARITHMETIC 


4. Practice Exercises on Reduction of Fractions 


Without 'pencil. Supply the 'missing numbers: 



(a) 

(6) (c) 

id) (e) 

(/) 

ig) 


1 - 
8 - 

? 

? ? 

f ? 

? 



- 56 - 

64 “ 48 

“ 24 “ 40 

- T2 - 

TO 


II 

_ S _ 

? 16 
15 r 

_ ? _ 20 
~ 30 r 

? 

32 

? 


3. f = 

12 

? 30 

49 “ ? 

? 24 

“ 4T ~ ? 

_ 18 

? 

TO 


Reduce both fractions in each group to fractions having a 

common denominator: 





(«) 


Q>) 

(c) 


(d) 


4. hi 


3 4 

4> 5 

1 5 
8j 6 


1 1 

3> 6 


5 2 3 

3) 5 


ii 

1 1 
81 4 


1 1 

2i 7 


ft 8 5 

O. 9, Q 


2 7 

3i TS" 

2 3 
3i 8 


3 5 

4i 6 


757 
*• 6 ? 8 


4 3 

9> 4 

3 5 
41 T 


f.f 


Reduce the following fractions to lowest terms: 



(a) 

(6) 

(c) 

id) ie) 

(/) 

(s') 

(/*) 

00 

if 

1 8 

28 

1 6 12 

32 IT 

2 7 

T6- 

1 5 

30 

28 

30 

9- U 

3 

T4 

1 8 

To 

72 9 

75 IT 

ff 

ff 

1 2 
20 

10. If 

13 . 

28 

1-8 

40 

TA 15 

42 T5 

TO 

A 

1 6 
18 

Reduce 

io whole 

or mixed 

numbers: 




11- if 

8 

3 

12 

4 

^ 2 7 

5 -8“ 

¥ 

¥ 

¥ 

12. ¥ 

4 8 

5 

19 

6 

-3 2. 4 5 

5 “8“ 

¥ 

¥ 

2 7 
9 

13. ^ 

4 3 

7 

1 6 
"T" 

4^ 

8 20 

1 8 

15 

36 

TO 

23 
1 8 



SEVENTH GRADE 


7 

Change to improper fractions: 


14. 5i 

8f 


3A 


7f 

2t 

7f 

16. 6f 

3| 



8| 

6f 

6| 

31 

Change to 12ths: 







16. 4 

6 

8 

9 

12 

3 

2 

1 


5. Review of Common Fractions 

If you find examples with common fractions hard to do, 
it may be that you cannot work with fractions as you 
should. By doing the examples in any one column that 
you may choose in this exercise, you can discover where 
you are weak. 



A 

B 

c 

D 

E 

1. Reduce to lowest 
terms: 

1 4 

32 

2 4 

■ 5 ^ 

4 5 

7 5 

1 6 

48 

3 4 

5^T) 

2. Supply the missing 
numerator: 

3 _ ? 

8 2 4 

5 _ ? 

T — T2 

9 — ? 
10 4 0 

6 — ? 
T“ 5^ 

3 _ ? 

3. Rewrite each group as 
like fractions: 

5 4 

S'; 5" 

6 4 
T; Z 

8 3 

9 ; 4 

5 6 

8; 7 

3 4 

T) T 

4. Reduce the following 
fractions: 

¥ 

1 5 

7 

1 8 

1 2 

-V- 

2 1 
■ 5 “ 

2 4 
20 

7 2 

5 6 

TS" 

4 8 

T5^ 

¥ 

2 9 

4 

2 6 

T¥ 

2 8 

7 

_8^ 

9 

5. Supply the missing 
number: 

7 = t 

9 = ¥ 

5 = V 

12=^ 

5=; 

6. Change to an improper 
fraction: 

12f 

16i 

14| 

18f 

i9i 


















8 


THE BAYNE-SYLVESTER ARITHMETIC 


6. Addition of Fractions 



Remember: 

1. Only like fractions may he added. 

2. Add only the numerators. 

3. Reduce the fraction in the answer to lowest terms. 

4. Check your work by going over it again. 

Without pencil. 

1. Alice earned $2j one afternoon and $f for an extra 
hour in the evening. How much did she earn that day? 

2. Mary weighed 87f lb. The next time she weighed 
herself she found she had gained f lb. How much did 
she weigh the second time? 

3. Fred carried home two packages. One weighed 
lb.; the other weighed 2| lb. What was the total 

weight of the packages? 

4. Walter walked to Robert’s home, a distance of 
2\ mi. Then both boys walked to Frank’s home, which 
was if mi. distant from Robert’s. How far had Walter 
walked when he reached Frank’s home? 

5. Alice practiced at the piano If hr. on Monday and 
if hr. on Tuesday. How many minutes did she practice 
all together? 









SEVENTH GRADE 


9 


7. Practice in Adding Fractions 

How many examples can you do correctly in 10 minutes? 
First, begin with Column A, and when you have finished, 
go on to Column B. Then try again, beginning with 
Column B and continuing to Column C. Each column 
has twenty examples. Don’t forget to turn the page. 


Without pencil. Write the answers only. 



A 

B 

c 

1. 

5 1 3 1 3 

12 ^ 12 ' 12 

_4 _ \ _3_[_ _7_ 

15 I 15 ^ 15 

3 1 2 1 4 

TO TO d- To 

2. 

2 1 2 I 1 I 1 

3 ^ 3^313 

5 I 3 I 7 1 1 

8 18 18^8 

4 _l_ 4 I 7 
Td-^d-T 

3. 

5 1 ^ 1 ^ 

6 ^ 6 ^ 6 

_3_ _|_1_1_7_ 

10 1 10 1 10 

5 4 _ 7 3 

8 4^ 8 ^ 8 

4. 

1 1 3 1 1 1 

10 "I 10 10 

4. _L 3 1 ^ 

9 r ^ 4 - 9 

3 1 5 _l_ 7 

1 2 T¥ 1 12 

6. 

A 4- i 

2 r 4 

i -1- i 

4 1 8 

T J- _1_ 

5110 

6. 

111 

3^6 

i + i 

5 1 1 

6^2 

7. 

i + i 

i + A 

i -1- A 

6 12 

8. 

i + i 

i -1 -1 

3 f 8 

1 -4- 1 

4 d- 5 

9. 

l + i 

1 4 _ iL 

317 

i + f 

Use pencil if needed. 



10. 

2 1 1 1 2 

3 -r 5 d" T5 

1 1 2 |_ 1 

6 13^ 

id-f 

11. 

i _ 4 - 1 -L i 

8 6 1 4 

1 _i_ 1 _4_ 1 

2 T" 6 T- 4 

1 1 1 1 1 

4 1 2 1 s' 

12. 

4 + 1 + 1 

1 + 1 + 4 

4 + 1 + 4 

13. 

71 + 2 + S-f 

6i + 8f+ 5i 

74 + 8|- + 21 

14. 

8f + If + 6f 

+ fif + If 

74 + 8f + If 


10 


THE BAYNE-SYLVESTER ARITHMETIC 


15. 7f+5|+9f 

16. 

17. 12i+6H8A 

18. 2j+2|^+4f 

19. 7^+8|^+5^ 

20. 3f+l^+6j 


5A+2A+6A 

6|+5j+3j 

4i+7A+8i 

5f+8f+6^ 

3i+7f+5i 

7f+94+3f 


c 

31^+61^+3^ 
2i+7i+7i 
3f+6i+9,% 
9f+6|+8*+6^ 
2^+6^+5j 
6| + 3y + 6f 


8. How to Use the Step-by-Step Test Drills 

On the next page you will find a step-by-step test drill. 

Under the direction of your teacher, begin with Exam¬ 
ple 1 in the column selected. Each column has a series of 
graded examples. Each example has a kind of difficulty 
in it differing from the one preceding it. Work as rapidly 
as you can, but make sure that each example is correctly 
done before you go to the next step. When you are told 
to stop, check your results with your teacher. If you 
have been careful, all your work will be correct. Aim to 
have no errors. If you get 100%, or a perfect score, it 
means that you have no difficulty in this part of arith¬ 
metic that you need worry about if you are careful here¬ 
after. 

If you ‘have made an error in any example, note care¬ 
fully its number on the test. Then do this example over, 
and to make sure that you will not fail on that difficulty 
again, do all the other examples on that step. This extra 
practice will help to strengthen you where you were 
weakest. 


SEVENTH GRADE 


11 


9. Step-by-Step Test Drill — Addition of Fractions 



A 

B 

C 

D 

E 

1. 

3 1 1 _1_ 2 

^ TO 

12~ 12“ 12 

2 13 11 
9^^ 9^- Q 

3 111 2 

8^8 V s' 

3 1 4 _1_ 5 

TT^ TT^TS 

2. 

7 4_ 3 2 

12 i 4 ^‘3 

3 111 6 
4121-8 

211 1 1 
■ 5 ^ 2^T-0 

2 1 3 ■ 11 

T^T5 

2 1115 

3 -^ 2^-6 

3. 

111 

8^2 

7 4_ 3 

TO- T 

.513 

8 r 4 

2 19 

3 ^ T 2 

5 11 

^ ^ "3 

4. 

5 2 _1_ 1 

■6 1 T 1 8 

2 _1_ 1 _J_ 5 

T ^ 2 1 T 

113 1 7 

2^ -S^T-O 

i + i + l 

2 1 3 _J_ 1 

T 1 5 - 1 2 

5. 

8-^- 

^15 


^T8 

6t\ 

8-=^- 

*^10 


2tV 

Q 2 
’^6 

6tV 

7 - 2 - 

4* 


3* 


2* 

3tt 

GtV 

6. 

6i 

8f 

IGtt 

12A 

8| 


12f 

6| 

9A 

fi 3 

Ott 

6| 


Zi 

5i 

GtV 

?A 

4| 

7. 

12f 

16i 

Gf 

9f 

121 


6i 

3tV 

171 

n 

2i 



8f 

GA- 

161 

16# 

8. 

15tV 

12| 

6f 

13i 

3 

-8- 



6 

71 

4f 

71 
• 2 


n 

18f 

18tV 

8 

6i 


1 

_ 2 


9 

Gj 

Ji 

9. 

151 


18i 

3| 

9f 


16| 

15h 

6f 

181 

6A 


Ji 

_Zi 

IM 

Ji 

ITf 

10. 

2G^ 

16| 


6| 

G-g- 


m 

9 

C5 
^ 6 

181 

9i 


H 

15^ 

7f 

51 

5 

-g- 


9 


6 

7 

GtV 


























12 


THE BAYNE-SYLVESTER ARITHMETIC 


10. Subtraction of Fractions 


A. 

B. 


C. 


60 

36| 1 

1 7 
•8 

I6i 

21 (3 + 18 ) 

7i 

25i 1 

2 

1 S' 


5 

52i 

Ilf 1 

f 

10 | 

16—8 

T 8 — 9 


Remember: 

1. Only like fractions may be subtracted, 

2. Subtract the numerators only. 

3. Reduce the fraction in the answer to lowest terms. 

4. Check your work by adding the remainder and the 
subtrahend. The result should equal the minuend. 


Without 'pencil. Write the answers only. 



(«) 

(6) 

(c) 

w 

1. 

1 1 

2 6 

5 _ 5 

7 7 

1 - i 

6-5A 

2. 

8 -4f 

1 _ 1 

4 12 

6| - 6i 

12| - 12 

3. 

"" 

71-2 

73 3 

<4—4 

12 4 

10 To 

4. 

9|-| 

9-8| 

Q 7_ _ 9 7 

— 1 

10 

5. 

3 1 

4 2 

7-3H 

9 7 

■§■ 8 

- 3 

6. 

1-i 

9f - 9 

Ql _ 3 
^8 8 

6f-4| 

7. 

li _ 2 
^3 3 

li-f 

li _ A 
^5 5 

If-I 

8. 

5 5 

8 8 

1 -i 

A _ 8. 

9 9 

1 — i 

9. 

7 1 

6 2 

Si 2 

®2 3 

8i - 8i 

If - If 

10. 

3j — 2f 

11 2 

12 3 

If - If 

4|-2i 








SEVENTH GRADE 


13 


11. Practice in Subtraction of Fractions 

How many examples can you do correctly in 10 minutes? 
First, begin with Column A, and when you have finished, 
go on to Column B. Then try again, beginning with 
Column B and continuing to Column C. Each column 
has eighteen examples. Don’t forget to turn the page. 


Use pencil if needed. 



A 



B 

( 


D 


1. 

8i - 

1 

3 

Syi ■ 

2 

3 

81 ^ - 

1 

2 

6 tV- 

-5f 

2. 

H - 

2 

3 

9i - 

3 

5 

H - 

8 f 

5^- 

1 

3 

3. 

12 f - 

2 

" ¥ 

7t^- 

- 6 i 

7J- 

2 

3 

n - 

6 f 

4. 

lOA 

-9f 

91 - 

8 ! • 

4i- 

3t 

8i- 

1 

2 

6. 

6 i - 

3! 

~ 

1 

2 

H - 

1 

3 

n - 


6. 


2 

3 

1 

00 

6 | 

li - 

3 

5 

H ~ 

1 

4 

7. 

n- 

2 

3 

9J - 

3 

5 

6 i- 

2 f 

li - 

2 

3 

8. 

8 f - 

7f 

6 f- 

K 4 

8 i - 

7f 

1 

00 

7f 

9. 

3f- 

1 

2 

li - 

1 

2 

a 8 

*T 2 

1 

" 6 

8 i - 

3 

10 

10. 

9f- 

2i 

7| - 

1 

3 

7f- 


6t^- 

1 

2 

11. 

4*- 

1 

" 3 

6f- 

Q 1 
’^12 

H- 

1 

3 

6i - 

1 

4 

12. 

8|- 

6i 


0 2 
“ ^T2 

9t^- 

- 

0 

li - 

1 

3 

13. 

9f - 

1 

8 

1? - 

3 

4 

liV- 

7 

1 2 

9A- 

7 

1 0 

14. 

1| - 

¥ 

lOf - 

3 

6 

— 

^ 8 

If 

li%- 

- li 

15. 

If- 

If 

8f- 

2i 

4t^- 

■ iiV 

9f- 

4! 

16. 

8f - 

2f 

5f- 

If 

If- 

u 

6i- 

1 

5 


14 


THE BAYNE-SYLVESTER ARITHMETIC 


A 

B 

c 

D 

17. 45| 

67f 

45i 

58| 


*3 

4 

5f 


18. 18f 

12i 

56* 

28f 

6§ 

7f 

2| 

7- 

' 3 


12. Step-by-Step Test Drill — Subtraction of Fractions 



A 

B 

c 

D 

E 

1. 

8 _ 2 
¥ ¥ 

1 1 _ 3 

T¥ T¥ 

7 3 

8 8 

9 _ 5 

T¥ T¥ 

7 _ 4 

T¥ T¥ 

2. 

3 5 

4 8 

1 _ 1 

3 ¥ 

9 _ 1 

10 5 

7 _ 1 
¥¥ ¥ 

1 1 _ 1 

T¥ 3 

3. 

9 1 

2 0 5 

9 _ 1 

2 4 8 

7 1 

12 4 

1 1 _ 1 

T¥ ¥ 

7 _ 1 

T¥ 2 

4. 

2_ 1 

¥ ¥ 

i_ 1 

2 ¥ 

5 1 

• 8 3 

4 _ 3 

5 4 

1 _ 1 

2 ¥ 

5. 

9 1 

T¥ 2 

4_ 2 

¥ T 

4 _ 1 

8 3 

6 _ 1 
¥ 2 

2 _ 2 

3 ¥ 

6. 

5 _ 1 
¥ 4 

8 _ 1 

¥ ¥ 

5 _ 3 
¥ 8 

5_ 3 

8 T¥ 

3_ 3 

4 T¥ 

7. 

6i-2t 

4t¥~ lyV 

^¥~3^ 

121-1 

18f-6f 

8. 

8|-2i 

9t-4i 

8H-61 

9f-6f 

7|-4* 

9. 

27-8f 

52-31 

46-91 

83-71 

46-51 

10. 

36tV-14tV 

85i-14f 

47*261 

79*-43* 

63*211 

11. 

16i-f 

37* I 

42i-T^ 

39*1 

23** 

12. 

ISi-llf 

00 

4*.|W 

1 

to 

bSh 

591-27* 

83i-21A 

.36*14* 

13. 

H-f 

n-i 

1*1 

11 — 1 

i^¥ 2 

11_3 

^10 T¥ 

14. 

82f 

271 

42i 

201 

241 

IM 

33i 

271 

78* 

i^¥ 













































SEVENTH GRADE 


15 


13. Multiplication of Fractions 


A. 3 X t = J/ = 2| 

R 3 V 1 — 9 

c. 2i X 3f = 

1 5 

3 7 

1 1 

B. 28-1 

8 

(1 X 8 = -^^ = 54) 

224 

2294 


Remember: 

1. Change mixed numbers to improper fractions. 

2. Cancel whenever possible. 

3. Multiply the numerators together for a new numerator 
and the denominators for a new denominator. 


Without pencil. 


(o) 

(&) 

(c) 

(d) 

1. ^ of 10 

I of 1 

i X 4 

f of 1 

2. I X 3 

3f X 1 

5J X 1 

4 X i 

3. 1 X 8 

|X2 

1 X 7 

7 A 3 

4. i X i 

7 of 9 

5 X i 

f of 1 

6. X 1 

iofi 

8 X 1 

6X4 


Use pencil if needed. 

6. Nellie needs f yd. of ribbon for each Christmas gift 

that she is making. For 6 gifts she will need-yards. 

7. Fred buys 60 papers each day at each. What 
does he pay for them? 






16 


THE BAYNE-SYLVESTER ARITHMETIC 


14. Practice in Multiplication of Fractions 

How many examples can you do correctly in 10 minutes? 
First, begin with Column A, and when you have finished, 
go on to Column B. Then, try again, beginning with 
Column B and continuing to Column C. 


Use pencil if needed. 


A 

B 

c 

D 

1. 5 X* 

18 X I 

X 18 

3 X f 

2. f X 6 

21 Xf 

15 Xf 

I X 12 

3. 27 X f 

f X25 

f X 35 

f X 36 

4 . 42 X f 

36 X 

28 X f 

If X 7 

6. i X f 

1 V 8 

4 ^ TT 

i V 9 
3^10 

1 V 1 5 

5 ^ re 

6 . f X J 

1 2 V 5 
T5 ^ ^ 

1 5 V 3 
^ ^ 5 

2 0 v/ 3 

2 1 5 

7 9 V ^ 

*• 10^9 

8 V ^ 
T5 ^ 8 

9 V 4 

20 ^ 9 

1 1 V 4 

1 6 1 1 

Q 1 8 V 1 5 

O. 25 ^ 24 

2 4 V/ 2 0 
25 28 

1 8 V 3 2 

40 ^ 45 

1 6 V 1 8 

^ A 20 

9. I X 1| 

I X li 

f X if 

f X If 

10. ^ X 4^ 

iVX3i 

i X If 

iX2i 

11. f X4f 

f X7i 

f X6f 

f X4f 

12. ^ X 6^ 

5| X 6f 

2f X 3f 

4f X3| 

13. A butcher’s price list was as follows: 


Lamb, 46cf per pound 
Ham, 32^ per pound 

Chicken, 42|zf per pound 
Turkey, 56^ per pound 


Steak, per pound Roast Beef (Prime), per 
pound 


SEVENTH GRADE 


17 


Find the cost of the following: 

(a) A leg of lamb weighing (d) Two chickens weigh- 

lb. ing 4j lb. each 

(b) A roast of beef weigh- (e) A turkey weighing 

ing 8f lb. 14^ lb. 

(c) One ham weighing 8f lb. (/) 3f lb. of steak 

16. Step-by-Step Test Drill — Multiplication of Fractions 



A 

B 

c 

D 

E 

1. 

iof 3 

iof 4 

tV of 3 

A of 6 

tV of 2 

2. 

12 X 1 

15 X f 

16 X 1 

20 X I 

16 X I 

3. 

I of 4 

tV of b 

f of 2 

Jof3 

A of 6 

4. 

f X 11 

f X 15 

Tlo X 9 

15 Xf 

16 X f 

5. 

6 X li 

3i X 7 

4 X li 

If X 5 

6 X 1| 

6. 

2i X 4 

3X1^ 

2iV ^ 6 

6 X 3A 

2| X 3 

7. 

3i X 8 

51 X 15 

18 X 2i 

2i X 24 

15 X 2i 

8. 

16 X ItV 

24 X 2i 

3i X 12 

20 X H 

2A X 18 

9. 

AXf 

5 V 4 

A i 

9 V 5 

A X A 

10. 

f Xf 

5 V 7 

T ^ 'S 

5 V 6 

1 V 8 

8 A y 

f X 1 

11. 

f X 

X 

CO 

1 X 4i 

Q2 V 7 
^3 ^ TO 

I X3f 

12. 

2+XI 

I X3| 

X A 

f X3| 

^A X 

13. 

3f X 2f 

5^ X 7| 

2i X 2f 

1| X 4| 

3| X 3J 

14. 

560 X 27| 

9261 X 78 

43f X 436 

276X247A 

58X5601 

15. 

fX2fX6 

fX4X3f 

6 JXIX 12 

8|^X 16XxV 

X 

X 
























18 


THE BAYNE-SYLVESTER ARITHMETIC 


16. Division of Fractions 


A. 

5_:_9 — _ 5 

8 • 8^2 — 

B. 4 1 

8.2 8 3 4 

9 ■ 3 9 % 3 “ 

3 1 

7 ^ 2i = J X ^ = 5 = 3 

1 

D. 1 1 

^ ^ " 3 4 

1 4 


Remember: 

1. The divisor follows the division sign. 

2. Change mixed numbers to improper fractions. 

3. Invert the divisor and multiply. 

4. Cancel whenever possible. 


Invert the following fractions: 


1. 

5 

8 

3 

4 

2 

7 

5 

9 

8 

1 1 

2 

3 

4 

5 

5 

9 

9 

1 0 

4 

9 

2. 

7 

5 

6 

8 

1 5 

1 6 

9 

1 1 

1 5 

7 

3 

2 

5 

7 

4 

3 

2 

4 

8 

2 

3. 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

6 

7 

8 

7 

4 

9 

1 2 

T5- 

3 

2 


Write as a 

fraction and invert: 





4. 

H 

4f 

^6 

8f 

4A 

6| 

5f 

7-^ 

* 8 

to 

6| 


An inverted fraction is called the reciprocal of 
the fraction. 


i is the reciprocal of 4 | is the reciprocal of f 

4 is the reciprocal of i f is the reciprocal of | 







SEVENTH GRADE 


19 


Write the reciprocal of each of the following: 


6. 

1 

7 

1 

8 

1 

9 

1 

2 

1 

4 

1 

3 

1 

5 

1 

6 

1 

TU 

1 

1 1 

6. 

4 

6 

7 

9 

3 

2 

12 

25 

16 

18 

7. 

3 

4 

2 

6 

11 

1 6 

1 9 

1 8 

1 6 

2 1 

7 

5 

5 

7 

T2 

1 7 

24 

2 7 

26 

T8 

8. 

1 8 

1 3 

2 7 

1 5 

1 9 

6 

1 7 

2 4 

1 6 

5 

5 


4 

2 

8 

3 

5 

"3“ 


2 


17. Practice in Division of Fractions 

How many examples can you do correctly in 10 minutes? 
First, begin with Column A, and when you have finished, 
go on to Column B. Then try again, beginning with 
Column B and continuing to Column C. 



A 


B 


c 

D 


1. 

1 

3 • 

3 

1 . 

4 • 

5 

i Q 

6 • 

1 . 

8 • 

2 

2. 

3 . 

8 • 

3 

6 . 

7 • 

2 


8 _ 
1 S 

- 2 

3. 

2 . 

5 • 

3 

4 

2 . 

3 • 

3 

4 

3 1 

7 • 2 

4 ^ 

1 

3 

4. 

2 

1 

5 

8 ^ 

1 

3 

0 . 3 

7 ^ 

4 

5 : 

5. 

9 

2 

7 

4 ^ 

4 

7 

1-1-1 

9 ^ 

9 

To 

6. 

12 H 

_ 1 5 

T6 

15 4 

_ 9 

10 

Q — At 

s . 

7 • 

1 

s 

7. 

6 _L. 

8 • 

1 

3 

3 . 

4 • 

1 

7 

1 . 7 

3*12 

1 . 

4 • 

7 

8 

8. 

1 

5 • 

9 

1 0 

5 

9 • 

1 

5 5 

14-7 

8 . 

9 • 

8 

T 

9. 

6 

7 • 

8 

1- 

10 

12 

1 

^ • 

1 

2 

10. 

1 _i_ 

S' • 

1 

4 

1 . 

6 • 

1 

s' 

^ ^ 

1 . 

2 • 

1 

7 

11. 

1 . 

4 • 

1 

5 

2 . 

3 • 

4 

3" 

4 8 

5 • 9 

3 _i_ 

T • 

1 2 

1 S 

12. 

1 . 

4 • 

1 

6 

1 . 

6 * 

1 

8 

1 _i_ 1 

10 * IS 

1 . 

4 • 

1 

TT 

13. 

1 . 

5 • 

1 

20 

1 . 

8 • 

1 

- 4 

6i ^ 

- 4 

14. 

H H 

- 2 

7 I 
‘ 2 ■ 

r 5 

6| 10 

3f H 

^ 5 


20 


THE BAYNE-SYLVESTER ARITHMETIC 


18. Step-by-Step Test Drill — Division of Fractions 



A 

B 

c 

D 

E 

1 . 

f 3 


1-4 

8 9 

T5 • ^ 

i - 7 

2 . 

i + 2 

§ - 3 

1 - 5 

i-5 

H -2 

3. 

f- 8 

f ^ 9 

f 4- 12 

1-15 

I - 6 

4. 

5 + if 

6 - if 

7H-ff 

8 + M 

4 - If 

5. 

10 H- 1 

12-1 

30 -J- f 

24 - I 

9 - i 

6. 

8 _i_ 2 

•9 • 3 

_9_ -i- 3. 
10*5 

1 _i_ 1 4 

8 • 24 

9 _i_ 3 

2 0 • 15 

2 1 _i_ 7 

^ 

7. 

3 . 3 

4 • 8 

4 4 

5 ' 15 

f T2 

8 8 

9 • ^ 

9 9 

^ 

8. 

1 . 1 

4 • 4 

i i 

i i 

1 _1_ 1 

T • T 

tV tV 

9. 

4i - 5 

21-4 

3i 5 

3f - 6 

2! - 7 

10. 

13i 9 

12i 5 

lOf - 7 

22i -f- 5 

7i- 12 

11. 

1 - If 

1 ^ 5i 

1 - 3| 

1 ^ If 

1 - 8i 

12. 

i!-i 

41 1 

^2 • 12 

Q2 1 

• 9 

tV 

^4 • 

13. 


11 6 

-*■8 • 8 


4| - f 

3i - I 

14. 

10 3i 

25 ^ 

14 - 2f 

8 - 4| 

15 - 12i 

16. 

8 1 1 
^ 

i - 1 # 

11 • ^2 

7 91 

TIT • ^3 

A - li 

16. 


t 

ii-4| 

M — 5|^ 

A-2f 

17. 

13i - U 

Ilf H- 2f 

6i -4f 

6J -r- 

3f — 1^ 





































SEVENTH GRADE 


21 


19. Principles of Fractions Reviewed 

1. Multiplying or dividing both the numerator and the 
denominator of a fraction by the same number does not 
change the value of the fraction. 

3 X 3 _ 9 9 3 _ 3 3 _ 9 

3X4 12 12^3 4 4 12 

Illustrate this principle with original examples. 

2. Multiplying the numerator of a fraction multiplies the 
fraction; multiplying the denominator of a fraction divides 
the fraction. 



2X1 _ 2 
3 3 


f = 2 X 4 


2X3 
1 _ 

6 ~ 


I -h 2 or I of I 


Illustrate this principle with a diagram, using the frac¬ 
tion ^ and the multiplier 2. 

3. Dividing the numerator of a fraction divides the frac¬ 
tion; dividing the denominator of a fraction multiplies the 
fraction. 



2^2 _ 1 _ _ 1 

3 3 6 ^23 

1 = 1 of f or 1^2 i = 2Xi 
























22 THE BAYNE-SYLVESTER ARITHMETIC 

Illustrate this principle with an original problem. Use 
a diagram. 

1. What are the two ways in which a fraction may be 
multiplied? 

2. Illustrate each with a diagram. 

3. What are the two ways in which a fraction may be 
divided? 

4. Illustrate each with a diagram. 

5. Tell which principle was applied in the solution of 
each of the following examples: 

w a ~ Y (c) f X 2 = -f- = 

(&) f = A (d) I - 3 = I X i = I 

6. Complete these statements: 

(а) Multiplying the numerator of a fraction - the 

fraction. 

(б) Dividing the numerator of a fraction _ the 

fraction. 

(c) Multiplying the _ of a fraction divides the 

fraction. 

(d) Dividing the_of a fraction divides the fraction. 

(e) Multiplying or dividing both the munerator and 

the denominator of the fraction by the same number_ 

_change the value of the fraction. 

(/) When we reduce a fraction to lowest terms, 
we —— both terms of the fraction by the same number. 

{g) When we reduce a fraction to higher terms, 
we-both terms of the fraction by the same number. 

7. Show with a diagram that f = f = tI* 

8. Show with a diagram that i = f = f * 







SEVENTH GRADE 


23 


20. Problems with Fractions 


1 . Mr. Ward employed 5 men in his business. These 
men were paid at the rate of $1.20 an hour, with time and 
a half for overtime. The regular working day is eight 
hours; on Saturday it is five hours. From the following 
card find (a) the amount due each man, and (b) the total 
amount of wages paid by Mr. Ward. (Change minutes to 
fractions of an hour.) 


Workman 

Monday 

Tuesday 

Wednesday 

1 

Thursday 

Friday 

Saturday 

A. 

7 hr. 30 min. 

7 hr. 

7 hr. 15 min. 

7 hr. 10 min. 

8 hr. 

8 hr. 

B . 

8 b-. 

8 h". 15 min. 

8 hr. 40 min. 

8 hr. 

9 hr. 

6 hr. 30 min. 

C. 

6 hr. 

6 hr. 45 min. 

6 hr. 15 min. 

6 hr. 50 min. 

7 hr. 10 min. 


D . 

8 hr. 10 min. 

8 hr. 20 min. 

8 hr. 50 min. 

8 hr. 45 min. 


6 hr. 

E. 

8 hr. 

7 hr. 45 min. 

7 hr. 20 min. 

8 hr. 

7 hr. 40 min. 

5 hr. 45 min. 


2. What must a dressmaker pay for each of the follow¬ 
ing supplies: 


(a) 5:^ yd. calico @ $.33f 

per yard 

(b) 6^ yd. gingham @ $.60 

per yard 

(c) 3 yd. organdie @ $.75 

per yard 

(d) 3f yd. percale @ $.40 

per yard 

(e) 16 yd. cotton voile @ 

$.62^ per yard 


(/) 8 yd. sateen @ $.87|- 
per yard 

(g) 5 yd. ribbon @ $.60 

per yard 

(h) 3| yd. lining @ $.75 

per yard 

(i) 7j yd. gingham @ $.66f 

per yard 

(j) 12 yd. silk @ $.25 per 

yard 


3. Mary made cookies to sell at a school fair. She made 
them from the recipes on page 24, using 4 times the quantity 
called for in the recipe for molasses cookies and 2j times 
the quantity called for in the recipe for oatmeal cookies. 
Rewrite each recipe as Mary used it. 

















24 


THE BAYNE-SYLVESTER ARITHMETIC 


Molasses 

J cup shortening 
i cup brown sugar 
f cup molasses 
1 egg, beaten 
^ cup boiling water 
cups pastry flour 


Cookies 

^ teaspoon soda 
j teaspoon salt 
1 teaspoon baking powder 
j teaspoon ginger 
^ teaspoon allspice 
I cup raisins 


Oatmeal Cookies 


1 cup shortening 
I cup sugar 
J cup coffee 
1 cup molasses 
I cup raisins 
i teaspoon cloves 

1 teaspoon 


2 cups graham flour 
2 cups pastry flour 
2 cups rolled oats 
^ teaspoon soda 
1 teaspoon baking powder 
1 teaspoon salt 
cinnamon 


4. Mr. Graham uses 1J T. of coal each month. At this 
rate, how ong will 12 T. last him? 

5. The postman delivered 4 packages of books to a 
school. The total weight was 12^ lb. What was the 
average weight of each package? 

6. The following are the records made by the same 
pupils at different times. Find the average record of 
each pupil. 


Broad Jump 



Fred Allen 

James L 

1st trial 

Gift. 

6i ft. 

2nd trial 

6f ft. 

7 ft. 

3rd trial 

7|ft. 

7i ft. 

4th trial 

7 ft. 

7i ft. 


SEVENTH GRADE 


25 


50-Yard Dash 


Ellen Hall 


Mary Wilkins 


1st trial 7^ sec. 

2nd trial 8 sec. 

3rd trial 7^ sec. 

4th trial 7f sec. 


8|- sec. 
8f sec. 
8f sec. 
8 sec. 


21. Selling Goods 


Mr. Price works at the silk counter in a large depart¬ 
ment store. After he sells material from a piece of goods, 
he enters on the ticket the amount of goods remaining on 
the piece. For example: One piece of silk measured 50 
yd. After selling 5^ yd., Mr. Price entered 44J yd. on the 
ticket. This showed that 44j yd. remained on the piece. 

1. How much remained on each of the following pieces 
of silk after each sale and after the day’s sales? 

Amount on Piece Day’s Sales 


8 yd., 3| yd., yd., 6f yd. 
4 yd., 6§ yd., 2^ yd. 


(a) 46j yd. 

(b) 18 yd. 

(c) 25j yd. 

(d) 34| yd. 

(e) 261 yd. 


6f yd., ^ yd., 7| yd., 2 yd. 
5| yd., 6J yd., 16| yd., 5 yd. 
^ yd., 6 yd., 3f yd., 4f yd. 


2. What amount must Mr. Price write on the sales 
check of each of the following customers: 

Mrs. A, who bought 4| yd. satin @ $1.75 per yard. 
Mrs. B, who bought 4f yd. rayon @ $.75 per yard. 
Mrs. C, who bought yd. taffeta @ $2.25 per yard. 
Miss D, who bought Sj yd. voile @ $.50 per yard. 
Miss E, who bought 3f yd. chiffon @ $2.25 per yard. 


26 


THE BAYNE-SYLVESTER ARITHMETIC 


22. Addition 


A. 

B. 

20,172 

492.0974 

6,248 

36.2 

926 

427. 

7 

.856 

53 

27.205 

12,938 

.8364 

20,172 

492.0974 


Remember: 

1. Write the figures in the proper column. 

2. When adding decimals, place decimal point under 
decimal point. 

3. Check your answer. The sum of each column when 
you add up should equal the sum when you add down. 


Without pencil. 
(a) 

Q>) 

(c) 

{d) 

1. 35 + 49 

73 + 64 

87 + 69 

4.7 + 2.3 

2. 68 + 23 

64 + 91 

58 + 87 

3.8 + 2.2 

3. 36 + 47 

53 + 72 

66 + 89 

5.4 + 1.6 

4. 42 + 29 

93 + 65 

57 + 78 

6.3 + 4.7 

5. 55 + 26 

62 + 77 

89 + 76 

5.5 + 2.5 


Rewrite in a column and add: 

6. .62 + 45.6 + 346.25 + .275 + 12.4 

7. 275.3 + .8642 + 347 + 25.275 

8. 936.04 + 7.2456 + .82 + 76 + 6.245 
*9. .34632 + 9.5 + .875 + 293 + 4.68 
10. 642.3 + 927.5 + .756 + 43.28 + .563 








SEVENTH GRADE 


27 


23. Harder Addition Combinations That Occur in 
Multiplication 

Time: 5 minutes. Aim: First time, perfect score; 
second time, perfect score in less than 5 minutes. 


Write the answers only. 




A 



B 



c 



D 


1. 

27 

+ 

8 

18 

+ 

7 

63 

+ 

7 

27 

+ 

4 

2. 

49 

+ 

4 

24 

+ 

9 

45 

+ 

8 

14 

+ 

6 

3. 

14 

+ 

7 

32 

+ 

5 

10 

+ 

6 

49 

+ 

5 

4. 

48 

+ 

5 

27 

+ 

9 

25 

+ 

8 

15 

+ 

6 

5. 

25 

+ 

9 

42 

+ 

5 

42 

+ 

7 

36 

+ 

9 

6. 

10 

+ 

3 

10 

+ 

2 

15 

+ 

8 

10 

+ 

5 

7. 

28 

+ 

5 

18 

+ 

9 

27 

+ 

6 

35 

+ 

7 

8. 

20 

+ 

6 

16 

+ 

8 

36 

+ 

7 

28 

+ 

6 

9 . 

15 

+ 

7 

36 

+ 

8 

16 

+ 

9 

48 

+ 

9 

10. 

20 

+ 

6 

56 

+ 

7 

14 

+ 

9 

49 

+ 

6 

11. 

12 

+ 

5 

45 

+ 

7 

64 

+ 

9 

25 

+ 

6 

12. 

27 

+ 

5 

20 

+ 

5 

24 

+ 

6 

40 

+ 

4 

13. 

30 

+ 

8 

49 

+ 

7 

35 

+ 

6 

24 

+ 

7 

14. 

64 

+ 

7 

35 

+ 

8 

30 

+ 

6 

48 

+ 

6 

15. 

45 

+ 

6 

56 

+ 

9 

54 

+ 

6 

45 

+ 

9 

16. 

15 

+ 

9 

18 

+ 

5 

49 

+ 

6 

27 

+ 

2 

17. 

25 

+ 

7 

54 

+ 

7 

20 

+ 

4 

16 

+ 

7 

18. 

49 

+ 

8 

40 

+ 

3 

32 

+ 

7 

20 

+ 

1 

19. 

12 

+ 

7 

18 

+ 

6 

28 

+ 

9 

64 

+ 

6 

20. 

56 

+ 

8 

48 


7 

28 

+ 

7 

54 

+ 

9 


28 


THE BAYNE-SYLVESTER ARITHMETIC 


24. Step-by-Step Test Drill — Addition of Integers 

The following examples contain the harder combinations 
in addition. 



A 

B 

C 

D 

E 

1. 

89 

58 

72 

75 

77 


57 

55 

48 

25 

24 


92 

88 

55 

88 

85 


98 

99 

58 

59 

55 


45 

77 

89 

87 

88 


58 

25 

94 

92 

99 


59 

85 

75 

48 

47 


87 



89 

89 

2. 

77,989 

437,697 

98,090 

67,699 

69,946 


87,978 

568,662 

58,705 

75,659 

77,874 


67,586 

459,956 

96,744 

68,729 

68,874 


87,747 

629,479 

89,527 

96,744 

53,485 


71,575 

689,778 

61,875 

76,735 

53,964 


57,698 

954,957 

67,667 

24,568 

36,530 

3. 

57,977 

91,755 

61,979 

78,469 

41,699 


95,778 

70,245 

29,781 

85,488 

77,978 


69,799 

56,757 

87,589 

56,690 

73,746 


79,774 

85,456 

89,866 

79,496 

69,679 


65,765 

25,585 

4V,995 

98,745 

74,546 


69,888 

76,476 

35,490 

60,248 

94,576 


86,310 

34,658 

98,828 

62,999 

98,779 






























SEVENTH GRADE 


29 


25. Step-by-Step Test Drill — Addition of Decimals 



A 

B 

c 

D 

E 

1. 

.4 + .1 + .3 

.3 + .1 + .5 

.6 + .1 + .2 

.2+.3 + .2 

.5+.1 + .3 

2. 

.8 + .2+.9 

.6+.5+.7 

.9 + .2+.3 

.9 + .8+.9 

.8+.7+.9 

3. 

.28 + .45 

.48 + .27 

.37 + .49 

.35 + .28 

.68 + .26 

4. 

.53 + .37 

.74 + .16 

.42 + .28 

.61 + .29 

.37 + .33 

5. 

.67 + .45 

.38 + .54 

.93 + .46 

.39 + .76 

.42 + .89 

6. 

.02+ .03 + 

.01 + .06+ 

.02 + .02 + 

.04 + .01 + 

.05 + .01 + 


.04 

.02 

.07 

.03 

.02 

7. 

.09 + .07 

.06 + .08 

.06 + .09 

.05 + .07 

.07 + .08 

8. 

.74 + .2 

.32 + .5 

.47 + .3 

.26 + .4 

.53 + .3 

9. 

32.4 + .64 

.925+2.5 

.37+2.45 

6.7+.275 

34.7+.98 

10. 

3 + 2.6 + 

46 + .9 + 

.175 +.2+ 

36+.64+ 

.8 + .62+ 


.75 

3.2 

8 

.2 

9 

11. 

645.6 

836.45 

.642 

32.8 

63.95 


.297 

9.2 

928. 

6.975 

.384 


38.37 

.836 

3.9 

438. 

286.5 


428. 

75. 

.38 

.29 

92. 







12. 

.25 + i 

.6 + f 

.14 + i 

.6 + i 

■4 + 1 




























30 


THE BAYNE-SYLVESTER ARITHMETIC 


26. Subtraction 


A. 

B. 

5407 Check 

64.2 Check 

609 

2.936 

4798 4798 

61.264 61.264 

609 

2.936 

5407 

64.200 


Remember: 

1. Write the figures in the proper column. 

2. When subtracting decimals, place decimal point under 
decimal point. 

3. Check your answer. The sum of the remainder and 
the subtrahend should equal the minuend. 


Without pencil. 

Find the difference between 

(a) (b) (c) (d) 

1 . 84 and 49 77 and 39 160 and 73 .6 and .45 

2. 78 and 83 29 and 85 75 and 130 .36 and .7 

3. 69 and 76 97 and 68 130 and 82 .05 and .025 

4. 15 and 94 37 and 95 35 and 110 1 and .85 

5. What must be added to 72.5 to make 80? 

6. What is the difference between 50 and 26.925? 

7. How much less than 9000 is .009? 

8. How much more than .75 is 750? 

9. Subtract 2.625 from 8000. 

10. The minuend is 924.6. The subtrahend is 62.475. 
What is the remainder? 

11. ? + 638.25 = 2002 

12. 2020.5753 - ? = 64.8 






SEVENTH GRADE 


31 


27. Step-by-Step Test Drill — Subtraction 



A 

B 

c 

D 

E 

1. 

15,357 

8,459 

17,535 

8,549 

17,535 

8,846 

15,753 

5,885 

15,375 

5,489 







2. 

14,634 

4,939 

14,643 

4,984 

14,364 

8,395 

13,446 

3,850 

14,643 

4,984 

3. 

17,579 

7,890 

15,797 

8,799 

17,759 

8,790 

17,975 

8,979 

15,779 

8,880 

4. 

16,335 

6,497 

13,653 

4,670 

15,336 

6,497 

16,335 

6,947 

13,653 

4,670 

5. 

13,835 

7,029 

13,853 

6,993 

15,338 

8,730 

15,833 

9,027 

3,358 

2,690 

6. 

133,641 

37,853 

113,364 

23,786 

164,133 

85,238 

113,436 

23,579 

136,341 

38,753 

7. 

117,732 

30,680 

113,727 

28,007 

112,737 

30,680 

72,731 

69,973 

137,172 

86,300 

8. 

121,844 

30,760 

144,821 

60,730 

124,814 

26,800 

81,442 

79,953 

142,481 

53,080 

9 

144,561 

57,861 

141,455 

60,786 

154,145 

56,079 

155,144 

59,058 

145,541 

78,561 

10. 

114,225 

44,148 

112,452 

35,382 

42,521 

41,744 

154,122 

83,415 

121,542 

43,842 







11. 

118,361 

89,276 

118,136 

58,928 

36,118 

27,589 

183,611 

92,759 

161,183 

75,893 










































































32 


THE BAYNE-SYLVESTER ARITHMETIC 


28. Step-by-Step Test Drill — Subtraction of Decimals 



A 

B 

C 

D 

E 

1 . 

.7 - .4 

. 8-5 

.9 - .2 

.7 - .2 

.9 - .7 

2 . 

.11 - .03 

.14 - .06 

.16 - .09 

.17 - .09 

.13 - .08 

3 . 

.8 - .45 

.9 - .27 

.6 - .43 

.7 - .42 

.9 - .38 

4 . 

5 . 

.58 - .53 

.37 - .34 

.87 - .82 

.69 - .61 

.57 - .52 

7 - .275 

9 - .624 

8 - .328 

4 - .275 

9 - .345 

6 . 

62.4 - 3 

9.27 - 6 

43.5 - 6 

87.2 - 4 

3.86 - 1 

7 . 

8 . 

.9 - .275 

.8 - .126 

.7 - .423 

.8 - .275 

.5 - .116 

.3 - .006 

.2 - .005 

.6 - .009 

.4 - .007 

.5 - .006 

9 . 

.73 - .2 

.95 - .4 

.64 - .3 

.83 - .5 

.97 - .4 

10 . 

624.228 

2.5 

926.645 

32.9 

428.295 

8.75 

346.27 

9.3 

84.695 

2.4 






11 . 

64.3 

2.875 

826.2 

27.375 

432.9 

7.125 

325.3 

3.625 

927.1 

46.875 






12 . 

200-.375 

700-.875 

300-.125 

800-.625 

900-.275 


































SEVENTH GRADE 


33 


29. Problems from Geography 


1 . In a certain year the following countries purchased 
goods from the United States to the amounts hsted: 


United Kingdom 
Canada . 
Germany. 
France 
Japan 


$840,066,000 

$835,878,000 

$481,581,000 

$228,746,000 

$257,582,000 


Italy . 
Argentina . 
Australia . 
Cuba . 
Netherlands 


. $131,650,000 
. $163,350,000 
. $159,126,000 
. $155,383,000 
. $148,268,000 


What was the total value of the goods exported by the 
United States to these countries? 

2. In the same year the United States imported goods 
to the amounts listed from the following countries: 


Canada . . . $475,077,000 Brazil . 

Japan . . $402,105,000 Germany 

United Kingdom $357,930,000 France. 

British Malaya . $277,784,000 China . 

Cuba . . . $256,552,000 Mexico 


. $203,018,000 
. $200,788,000 
. $167,788,000 
. $151,680,000 
. $137,815,000 


What was the total value of the imports from these 
countries? 

3. In 1927, exports from the United States amounted to 
$4,864,805,773. Imports amounted to $4,184,378,182. 
How much greater was the value of the exports than the 
value of the imports? 

4. The following table shows the percentage of fruit 
and vegetables supplied to the United States by the three 
states ranking highest in the amount supplied. Find for 
each commodity (a) the total per cent supplied by the 
three states; (b) the per cent supplied by all the other 
states combined. 



34 


THE BAYNE-SYLVESTER ARITHMETIC 


Commodity 

First 

Second 

Third 

Apples. 

Grapes. 

Peaches.... 
Grapefruit.. 
Lemons.... 
Oranges.... 
Potatoes.. . . 

Washington 31.2% 

California 93.8% 

Georgia 44.4% 

Florida 92.1% 

California 99.7 % 

California 66.4% 

Maine 19.6% 

New York 17.4% 
New York 2.7% 
California 13.1% 
California 3.7% 

Idaho 7.5% 

Michigan 2.3% 
N. Carolina 7.1% 
Texas 3% 

Florida 32.7% 
Texas 13.9% 

Alabama .5% 

New York 12.7% 


5. The amount of snowfall in New York City during a 
recent winter was as follows: December, 2.4 in.; January, 
3.1 in.; February, 4.0 in.; March, 4.8 in. What was the 
total for the season? 

6. The longest river in Africa is the Nile, which is 
3670 mi. long. The Ob, the longest river in Asia, is 3235 
mi. long. How much longer is the Nile than the Ob? 

*7. The highest point in Africa is Mt. Killimanjaro, 
which has an altitude of 19,318 ft. The lowest point is 
in the Libyan Desert and is 440 ft. below sea level. What 
is the difference in altitude between the highest and the 
lowest point in Africa? 

*8. The highest point in Asia is Mt. Everest, which 
has an altitude of 29,141 ft. The lowest point is on the 
Dead Sea, which is 1293 ft. below sea level. What is the 
difference in altitude between the highest and the lowest 
point in Asia? 


9. 

Africa 

Asia 

Dif¬ 

ference 

Area 

11,510,597 sq. mi. 

17,512,000 sq. mi. 

? 

Population 

157,645,000 

902,094,774 

? 



















SEVENTH GRADE 


35 


10. Lake Superior, in the United States, has an area of 
31,200 sq. mi. The area of Lake Victoria Nyanza, in 
Africa, is 967 sq. mi. more. What is the area of Lake 
Victoria Nyanza? 

11. Mt. Everest, in Asia, is 29,141 ft. high. Mt. 
McKinley, in Alaska, is 20,464 ft. high. What is the 
difference in altitude between Mt. Everest and Mt. 
McKinley? 

12. The length of the four longest rivers in Africa is as 
follows: Nile, 3670 mi.; Congo, 2800mi.; Niger, 2600mi.; 
Zambezi, 1600 mi. (a) Find the total length of these 
four rivers, (h) Find the difference between the longest 
and the shortest river. 

13. The length of the ten longest rivers in Asia is as 
follows: 


Ob ... . 3235 mi. 

Yangtze-kiang . . 3000 mi. 

Lena. 2860 mi. 

Amur .... 2700 mi. 
Mikong .... 2600 mi. 


Yenesei 
Hwang-ho . 
Indus. 

Brahmaputra 
Ganges . 


. 2500 mi. 
. 2300 mi. 
. 2000 mi. 
. 1800 mi. 
. 1455 mi. 


What is the total length of these ten rivers? 


14. Make up a problem using the information given in 
Problem 13. 

15. Make up a problem using the information given in 
Problems 12 and 13. 

16. Australia has a population of 9,263,372 and an area 
of 3,455,395 sq. mi. Find the difference in population 
and area between Asia and Australia. (See Problem 9 
for needed facts.) 




36 


THE BAYNE-SYLVESTER ARITHMETIC 


30. Multiplication 


A. 62.4 

7 

B. 

84 

.06 

C. .036 
.003 

436.8 

5.04 

.000108 

D. 


E. 

Checks 

10 X 62.48 = 624.8 

6.2 (1) .4 (2) 6.2 

100 X 62.48 = 6248. 

.4 

6.2 /4.)2/4.8 

1000 X 62.48 = 62480. 

2.48 

2.48 


Remember: 

1. To multiply decimals, multiply as with whole numbers. 
Then, beginning at the right of the product, point off as many 
decimal places as there are decimal places in multiplicand 
and multiplier together. 

2. Prefix as many zeros as are needed to fill out the re¬ 
quired number of decimal places. 

3. To multiply by 10, 100, 1000, etc., move the decimal 
point as many places to the right as there are zeros in the 
multiplier. 


Without pencil. 



(a) 

ih) 

1. 

3 X .3 

3 X .03 

2. 

6 X .7 

6 X .07 

3. 

5 X .2 

5 X .02 

4. 

8 X .4 

8 X .04 

5. 

.6X4 

.7X4 

6. 

.02 X 5 

.2 X .4 



(c) 



{d) 


3 

X 

.003 

.4 

X 

2 

6 

X 

.007 

6 

X 

.5 

5 

X 

.002 

6 

X 

.05 

8 

X 

.004 

6 

X 

.005 

.8 

X 

5 

.4 

X 

5 

.3 

X 

.09 

.02 

X 

.04 










SEVENTH GRADE 


37 


(a) 

(b) 

(c) 

(d) 

7. .04 X 8 

.6 X .4 

.6 X .07 

.05 X .02 

8. .06 X 5 

.08 X .7 

.5 X .08 

.06 X .08 

9. .08 X 5 

.09 X .6 

.6 X .09 

.06 X .05 

*10. 1 of .1 

1 of .2 

A of .8 

i of .6 

*11. f of .8 

f of .4 

I of 2.4 

I of 6.4 

These examples include all the harder multiplication 
combinations. Can you score 100%? 

With pencil. 

(a) 

(b) 

(c) 

(d) 

12. 6870 

4076 

8609 

9708 

78 

89 

87 

76 

13. 6078 

6704 

9068 

8079 

708 

809 

607 

608 

14. 9680 

8709 

4760 

6087 

345 

967 

892 

978 

16. 9604 

9780 

8750 

5896 

679 

406 

805 

308 

16. 38,746 

67,890 

86,569 

96,807 

879 

467 

607 

687 

17. 80,467 

98,760 

96,087 

12,345 

596 

798 

846 

908 


























38 


THE BAYNE-SYLVESTER ARITHMETIC 


31. Drill on the Difficult Multiplication Combinations 

Time: 5 minutes. Aim: First time, a perfect score; 
second time, a perfect score in less than 5 minutes. 

Write the answers only. 



A 

B 

c 

D 

1. 

8X0 + 3 

0X9 + 8 

0X5 + 4 

0X2 + 4 

2. 

7X8 + 8 

9X0 + 6 

8X8 + 9 

8X6 + 5 

3. 

0X3 + 4 

0X7 + 2 

6X0 + 6 

7X6 + 7 

4. 

4X0 + 4 

4X9 + 7 

4X0 + 4 

9X0 + 4 

5 . 

9X6 + 7 

6X0 + 4 

5X0 + 2 

9X6 + 6 

6 . 

2X0 + 1 

7X9 + 7 

6X9 + 6 

1X0 + 6 

7. 

8X8 + 7 

8x7 + 7 

2X0 + 5 

9X4 + 9 

8 . 

0X2 + 5 

0X1 + 4 

8X7 + 9 

0X8 + 3 

9 . 

0X4 + 6 

5X0 + 8 

7X0 + 3 

0X1 + 6 

10. 

6X8 + 6 

5X0 + 5 

7X8 + 9 

6X8 + 9 

11. 

8X0 + 4 

7X0+1 

4X0 + 2 

9X0 + 8 

12. 

9X4 + 8 

9X6 + 9 

1X0 + 3 

4X9 + 9 

13. 

0X8 + 4 

6X9 + 9 

6X8 + 7 

0X3 + 5 

14. 

8X6 + 9 

0X1 + 6 

6X0 + 8 

3X0 + 2 

15 . 

7X0 + 6 

7x6 + 9 

0X4 + 3 

0X7 + 3 

16 . 

7X8 + 7 

1X0 + 4 

6X7 + 5 

9X7 + 7 

17 . 

0X2 + 1 

8X6 + 6 

0X2 + 6 

0X3 + 8 

18 . 

4X9 + 8 

0X9 + 2 

8X6 + 7 

9X4 + 7 

19 . 

3X0 + 5 

6X8 + 5 

0X7 + 5 

8X0 + 6 

20. 

8X7 + 8 

0X8+1 

6X9 + 7 

6X7 + 7 


SEVENTH GRADE 


39 


32. Placing the Decimal Point in Multiplication 

What is the rule for placing the decimal point in the 
product when multiplying decimals? 

Rewrite the answers given in the following exercise and 
complete them by placing the decimal point in the proper 
place. Work for a perfect score: 


1. 83.6 X 2.46 = 205656 

2. 83.6 X 24.6 = 205656 

3. 836 X 24.6 = 205656 

4. 83.6 X .246 = 205656 

5. 836 X 2.46 = 205656 

6. .836 X 2.46 = 205656 

7. .836 X 246 = 205656 

8. 836 X 246 = 205656 

Select the correct product. 
Example 

17. 32.5 X 434 

18. 325 X .434 

19. .325 X .434 

20. 3.25 X 4.34 

21. 32.5 X 4.34 

22. 32.5 X 43.4 

23. 32.5 X .434 

24. 325 X 4.34 

25. 3.25 X .434 

26. 3.25 X 434 

27. .325 X 434 

28. 325 X 43.4 


9. 8.36 X 24.6 = 205656 

10. .836 X 24.6 = 205656 

11 . 8.36 X 2.46 = 205656 

12. 8.36 X .246 = 205656 

13 . 836 X .246 = 205656 

14 . .836 X .246 = 205656 

15 . 83.6 X 246 = 205656 

16 . .0836 X 2.46 = 205656 

Try for a perfect score: 


14105.0 

14105.0 

.141050 

1410.50 

141.050 

141.050 

141.050 

1410.50 

141.050 

14105.0 

1410.50 

.141050 



Products 

141.050 

1410.50 

141.050 

1.41050 

14105.0 

141.050 

14.1050 

1.41050 

14105.0 

1410.50 

14.1050 

1410.50 

14105.0 

14.1050 

14.1050 

.141050 

1.41050 

1410.50 

1410.50 

14.1050 

141.050 

141050 

1.41050 

14105.0 


40 


THE BAYNE-SYLVESTER ARITHMETIC 


33. Problems in Multiplication 

1. A rod equals 16.5 ft. How many feet are there in 
12.5 rd.? 

2. The average monthly rainfall in New York for one 
year was 4.14 in. What was the rainfall for the year? 

3. An automobile averages 26.5 mi. an hour. At this 
rate, how far will it travel in 16.5 hr.? 

4. A laundry charges $.60 a dozen for towels. What 
will be the bill for 28 towels at this rate? 

5. A gallon of milk weighs 8.6 lb. What is the weight 
of 45.5 gal.? 

6. An airplane averaged 142.6 mi. an hour for 4.5 hr. 
How far did it travel in that time? 

7. A train averaging 46.25 mi. an hour will travel- 

mi. in 14.25 hr. 

8. Multiply by 10: .6, 27.5, .46, 320, .086 

9. Multiply by 100: 3.64, 4.26, 53.6, .6, .275 

10. Multiply by 1000: 46.2, .0568, 53.2, 6.45, .2785 

Find the cost of 

11. 24 lb. lard @ $.195 per pound. 

12. 3.5 yd. ribbon @ $.85 per yard. 

13. 58 bu. potatoes @ $.936 per bushel. 

14. 75 bu. wheat @ $1.16 per bushel. 

15. 15 T. hay @ $10.60 per ton. 

16. 25 T. coal @ $14.50 per ton. 

17. 100 ft. wire @ $.025 per foot. 

18. 1000 ft. fence wire @ $.125 per foot. 

19. In a motorboat race at Detroit, one entrant aver¬ 
aged 55.65 mi. per hour. How many miles did he travel 
in 2.4 hr.? 


SEVENTH GRADE 


41 


34. Step-by-Step Test Drill — Multiplication of Decimals 



A 

B 

C 

D 

E 

1 . 

780.6 

8 

60.47 

9 

.8609 

7 

8.709 

6 

84.97 

7 






2 . 

623 

.42 

7456 

6.9 

8346 

7.2 

8746 

.69 

3945 

.72 






3 . 

8645 

2.8 

945.6 

65 

8325 

7.8 

459.6 

45 

8295 

7.8 






4 . 

48 

.25 

.75 

28 

.64 

25 

84 

.75 

.25 

5 . 

364.5 

.58 

92.75 

.56 

329.5 

.84 

69.35 

.86 

936.5 

.46 






6 . 

8.79 

.004 

.687 

.08 

60.79 

.006 

8.326 

.009 

45.68 

.007 






7 . 

.0125 

.75 

.0875 

.25 

.0625 

.65 

.0375 

.43 

.0268 

.36 

8 . 

7.06 

.025 

80.92 

.075 

40.62 

.075 

8.024 

.05 

62.08 

.075 





9 . 

1 of .72 

f of.56 

i X .32 

f X .63 

iX .45 

10 . 

100 X.046 

1000 X 
.0375 

10 X.096 

100 X.0642 

1000 X 
.0625 

11 . 

1000X82.6 

100X46.8 

37.5X100 

1000X6.42 

1000X2.68 























































42 


THE BAYNE-SYLVESTER ARITHMETIC 


35. Division 


A. .8 

8)6.4 

B. .003 

5).015 

C. 1.7 

l/5.)2/5.5 

D. 3120. 

{002.)qJM0. 

E. 312000. 

/002.)624/000. 

F. 1.274 

6000)7.644/ 


Remember: 

1. Make the divisor a whole number by moving the 
decimal point to the right, 

2. Move the decimal point in the dividend as many 
places to the right as there are decimal places in the divisor. 

3. Place the decimal point in the quotient. 

4. Divide as in division by a whole number. 

5. When dividing by 10, 100, 1000, or their multiples, 
cross out the zeros in the divisor and move the decimal point 
in the dividend as many places to the left as there are zeros 
in the divisor. 

6. Check your work by multiplying the quotient by the 
original divisor. 


Without pencil. 
Give the quotient: 


(a) 

(6) 

(c) 

(d) 

(e) 

1. 3)6.3 

.06)772 

5)4“ 

1.1)5.5 

4):8' 

bo 

.5)2“ 

.2):^ 

.2).18 

7)3.5 

3. 6). 12 

2)4.2 

.12).84 

.4) .32 

1.2yL2 


















SEVENTH GRADE 43 


(a) 

(h) 

(c) 

id) 

(e) 

4. 7)^ 

sW 

.8)4 

i2yr 

.8)4.“ 

6. 6)3“ 


.12)48 

.5W 

.5)2“ 

In the following examples, write only the first figure of 

the quotient: 





(a) 


(b) 

(e) 

(d) 

6. 43)478 


42)864 

57)^ 

26)437 

7. 68)M3 


47)436 

57)1756 

77)mi 

8. 43)^ 


52)453 

42)8^ 

63)493 

9. 34)^ 


42)4l8 

64)^ 

72)718 


With pencil. 


10. 63,878 325 = ? 

11. ? X 43 = 9245 

12. 47 X ? = 32,477 

13. 45,926 ^ 37 = ? 

14. ? X 78 = 79,248 

15. 92,645 428 = 

22 . 

23. 

24. 


16. ? X 54 = 108,432 

17. 83 X ? = 170,980 

18. 131,126 ^ 262 = ? 

19. 60,231 75 = ? 

20. 13,515 27 = ? 

21. 129,440 ^ 16 = ? 
.624, 624, .0624 


? 

Divide by 10: 72.4, 6.24, 

Divide by 100: 3246, 324.6, .3246, 32.46, 3.246 
Divide by 1000: 4598, 45.98, .4598, 4.598, 459.8 


26. 246.3 600 

26. 82.45 H- 7000 

27. 2457 ^ 900 

28. 456.8 -4- 2000 


29. 324.5 H- 2700 

30. 564.8 ^ 5200 

31. 5.648 6500 

32. 4.983 ^ 4600 



44 


THE BAYNE-SYLVESTER ARITHMETIC 


36. Buying by the Hundred and the Thousand 

What does the Roman number C stand for? The 
Roman number M? The abbreviation cwt.l 

What is the cost of 850 envelopes at $2.50 per hundred? 



$2.50 

Divide 850 by 100. 

8.5 

850 - 100 = 8.5 

1250 

8.5 X $2.50 = cost of envelopes 

2000 


$21,250 


What must Mr. Lucas pay for 5300 ft. of Georgia pine 
at $65 per thousand feet? 



$65 

Divide 5300 by 1000. 

5.3 

5300 1000 = 5.3 

195 

5.3 X $65 = cost of pine 

325 


$344.5 = $344,50 


Find the cost of the following: 

1. 6000 lb. of sugar at $6.25 per cwt. 

2. 2500 cigars at $6.50 per C. 

3. 1400 lb. of freight shipped at the rate of $.35 per 
cwt. 

4. 7500 laths at $.75 per C. 

5. 2500 cu. ft. of gas at $1.20 per M. 

6. 2650 ft. of yellow pine at $48 per M. 

7. 15,200 ft. of oak flooring at $115 per M. 







SEVENTH GRADE 


45 


8. 7200 envelopes at $4.25 per M. 

9. 2600 lb. of hay at $1.20 per cwt. 

10. 1500 lb. of maple sugar at $19 per cwt. 

11. 800 lb. of honey at $12.50 per cwt. 

12. 500 ice-cream cones at $.95 per C. 

13. A hundred-pound sack of sugar costs $6.25. What 
is the cost of one pound? 

14. Mary bought 100 ft. of chicken wire for $6. What 
was the cost per foot? 

15. Mr. Brown has a 100-acre farm which he planted 
in wheat. His crop amounted to 3462 bu. What was 
the average yield per acre? 


37. Review of Difficult Combinations in Division 

These examples supply -drill on hard combinations. 
Can you score 100%? Don’t forget to turn the page. 


Write the answers 

: only. 



A 

B 

C 

D 

1. 7)^ 

2)182 

1)91260 

4)3224 

2. 4)284 

4)4^ 

4)3628 

5)1040 

3. 2)162 

5)405 

6)546 

3)2703 

4. 5)400 

6)654 

5)5400 

2)216 

5. 1)36102 

7)707 

6)186 

6)5418 

6. 6)306 

8)6424 

7)350 

7)357 























46 THE BAYNE-SYLVESTER ARITHMETIC 


A 

B 

c 

D 

7. 9)5409 

6)1842 

8)8064 

3)1836 

8. 4)2436 

9)6390 

4)436 

1)16209 

9. 4)2832 

1)9339 

6)4218 

8)2480 

10. 8)5608 

3)6183 

1)21069 

6)3042 

11. 7)W7 

4)2i4 

6)4824 

2)m 

12. 6)3054 

8)4824 

9)7236 

5)100 

13. 9)5409 

4)8^ 

7)7056 

6)4248 

14. 2)1618 

9)4554 

3)1860 

9)5445 

16. 6)2^ 

7)3507 

8)6448 

7)5635 

16. 3)3027 

9)9072 

4)832 

6)2448 

17. 4)368 

5)1()5 

9)3645 

9)9360 

18. 8)8560 

9)4536 

1)62013 

4)288 

19. 6)4824 

9)6354 

9)7263 

5)M() 

20. 1)16023 

7)7056 

2)1816 

9)6372 













































SEVENTH GRADE 


47 


38. Selecting the Quotient 


Select the correct quotient. Try for a perfect score: 



Example 


Quotients 


1. 

.135042 317 

.000426 

.0426 

.426 

4.26 

2. 

135042 .317 

426000 

426 

.426 

42.6 

3. 

135.042 ^ .317 

4260 

426 

.0426 

4.26 

4. 

13.5042 H- 31.7 

.426 

.0426 

42.6 

4.26 

5. 

13.5042 ^ 3.17 

426 

4.26 

.426 

42.6 

6. 

1.35042 ^3.17 

42.6 

.426 

.0426 

4260 

7. 

13504.2 317 

.426 

42.6 

426 

4.26 

8. 

13.5042 ^ 317 

.0426 

426 

.426 

4260 

9. 

135042 ^ 31.7 

42.6 

4.26 . 

4260 

.426 

10. 

.135042 -h 31.7 

426 

.00426 

.0426 

42.6 

11. 

13504.2 ^ 31.7 

426 

4260 

4.26 

.426 

12. 

1350.42 ^ 31.7 

42.6 

.426 

4260 

.0426 

13. 

.135042 3.17 

.0426 

.426 

.00426 

4.26 

14. 

1350.42 317 

.426 

42.6 

.0426 

4.26 

15. 

13.5042 4- .317 

.426 

42.6 

.0426 

426 

16. 

135.042 4 - 317 

4.26 

.426 

426 

42.6 

17. 

1.35042 4 - .317 

4.26 

.00426 

.426 

4.26 

18. 

1.35042 4 - 317 

.00426 

.0426 

4.26 

42.6 

19. 

135042 4 - 3.17 

.426 

42600 

42.6 

.0426 

20. 

135042 4 - 3.17 

42600 

42.6 

.426 

.0426 

21. 

.135042 4 - .317 

.426 

4260 

42.6 

4.26 

22. 

135.042 4 - 31.7 

4.26 

42.6 

.426 

4260 

23. 

1.35042 4 - 31.7 

.0426 

.426 

42.6 

4.26 

24. 

1.35042 4 - -0317 

.0426 

.00426 

42.6 

4.26 


48 


THE BAYNE-SYLVESTER ARITHMETIC 


39. Step-by-Step Test Drill — Division of Decimals 

Do not carry the quotient beyond three decimal places. 



A 

B 

C 

D 

E 

1. 






73)$91.25 

57)$402.47 

26)$220.48 

54)$178.58 

24)$200.64 

2. 






63)516.6 

53)397.5 

76)623.2 

63)592.2 

57)454.6 

3. 






58)96.834 

53)83.245 

76)86.485 

42)82.936 

37)96.456 

4. 






95)6.3458 

89)7.5823 

79)6.9365 

98)8.4626 

67)6.2456 

5. 






78).2364 

77).2562 

38).2453 

56). 1764 

28). 1952 

6. 






75)244.5 

28)107.8 

55)110.1 

34)130.9 

46)177.1 

7. 

$64 25 

$42 24 

$95 4- 52 

$108 ^ 48 

$60 - 48 

8. 

327 36 

456 ^ 35 

920 27 

729 ^ 56 

398 - 36 

9. 

6324 H- 37 

8336 52 

8208 54 

9394 H- 36 

8496 - 53 

10. 

a 

4 5 

ff 

4 3 

5T 

2 4 

2-S 

11. 

w 

8 2 
■43- 

p 

if 

32 

T8 

12. 






6.2)6.246 

.28).8235 

2.3)5.827 

.38)9.286 

2.1).4532 

13. 

8.5)268 

3.2)925 

7.3)645 

9.4)468' 

6.5)834' 

14. 

.326)24:8 

.236)“5:35 

.436)327.2 

.924)875.3 

.648)4^ 

15. 

624-^1600 

843-^2500 

4383600 

479-9000 

927^-5000 


































































SEVENTH GRADE 


49 


40. Problems about Rainfall 

In the following table you will find the monthly rainfall, 
in inches, in certain cities in 1928: 


Station 

Jan. 

Feh. 

Mar. 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Albany. 

2.6 

2.5 

2.7 

2.4 

3.0 

3.8 

3.9 

4.0 

3.2 

3.0 

2.8 

2.6 

Atlanta. 

4.9 

4.8 

5.3 

3.6 

3.5 

3.8 

4.7 

4.4 

3.0 

2.6 

3.0 

4.7 

Boston. 

3.6 

3.4 

3.6 

3.3 

3.2 

2.9 

3.5 

3.6 

3.1 

3.2 

3.3 

3.4 

Chicago. 

2.0 

2.2 

2.6 

2.9 

3.4 

3.7 

3.6 

2.9 

3.0 

2.6 

2.5 

2.1 

Denver. 

0.4 

0.5 

1.0 

2.1 

2.2 

1.4 

1.7 

1.4 

1.0 

1.0 

0.6 

0.7 

Galveston. 

3.4 

2.8 

2.7 

3.1 

3.4 

4.4 

3.7 

4.3 

5.6 

4.4 

3.3 

3.8 

Los Angeles. 

2.8 

2.9 

3.0 

1.1 

0.5 

0.1 

0.0 

0.0 

0.1 

0.8 

1.5 

2.9 

Mobile. 

4.8 

5.3 

6.0 

4.6 

4.3 

5.4 

6.0 

5.9 

5.0 

3.6 

3.6 

5.4 

New Orleans. 

4.3 

4.2 

4.7 

5.2 

4.6 

5.9 

6.4 

5.8 

5.0 

3.3 

3.1 

4.8 

New York. 

3.8 

3.7 

4.1 

3.3 

3.2 

3.3 

4.5 

4.5 

3.6 

3.7 

3.4 

3.4 

Pittsburgh. 

2.9 

2.7 

3.0 

2.9 

3.3 

3.9 

4.4 

3.2 

2.5 

2.4 

2.6 

2.7 

Seattle. 

4.9 

3.7 

2.7 

2.4 

1.8 

1.4 

0.6 

0.6 

1.7 

2.7 

5.3 

5.4 


1. Find the total yearly rainfall in each city. 

2. Find the average monthly rainfall in each city. 

3. Rearrange the cities according to the total rainfall, 
placing the city with the greatest amount at the top. 

4. Which city had the greatest rainfall in each month? 

5. Which cities had the same amount of rainfall for 
December? For November? For September? For 
June? 

6. What is the difference between the rainfall for 
January and June for the following cities: Denver, Los 
Angeles, Mobile, Atlanta, New York? 

7. Which city had less than one inch of rainfall during 
five consecutive months? 









































50 


THE BAYNE-SYLVESTER ARITHMETIC 


41. Practice with Decimals 

1. Find the difference between six tenths and six 
hundredths. 

2. How much more than fifteen hundredths is fifteen? 

3. Arrange the following numbers in order of size, 
writing the number of least value first: 

64.4 6.044 64.04 4604 6.44 .644 600.4 

4. Three thousandths plus three thousand equal- 

5. Rewrite the following in words: 4.62, 46.2, .462, 
.0462, 4620. 

6. How much must be added to eight thousandths to 
make eight hundredths? 

7. How much less than one is one thousandth? 

8. Change the common fraction seven eighths to a 
decimal fraction. 

9. Change the decimal twenty-five hundredths to a 
common fraction. 

10. Rewrite as decimals and find the sum: three tenths, 
eight thousandths, five, six and fifty-five hundred thou¬ 
sandths. 

11. What happens when a zero is annexed at the right 
of a whole number? 

12. What happens when a zero is annexed to the last 
digit of a decimal fraction? 

13 . Which is larger: .7 or .69? 

14 . How many decimal places are there in the product 
of 3.06 and .29? 

16 . What happens when the decimal point in a num¬ 
ber is moved one place to the right? What happens 
when it is moved one place to the left? 



SEVENTH GRADE 


51 


42. What You Should Know about Decimals 

Supply the missing words: 

1. Any digit in a decimal represents ten times as much 

in value as the same digit in the next place to the_ 

2. Any digit in a decimal represents_as much in 

value as the same digit in the next place to the left. 

3. A_to the right of the last digit in a decimal 

does not change the value. 

4. The zero in 0.3 does_change the value of the 

decimal. 

5. When adding decimals, place i _ under 

6. When subtracting decimals, place the_in 

the subtrahend exactly under the_in the_ 

7. To multiply by 1000, move the decimal point_ 

places to the_ 

8. To divide by 100, move the decimal point _ 

places to the_ 

9. When multiplying decimals, multiply as with 

integers and point off in the_as many decimal places 

as there are decimal places in both-and- 

10. To divide a decimal by a decimal, move the decimal 

point in the_as many places to the-as there are 

decimal places in the divisor. Then place the decimal 
point in the quotient over the decimal point in the- 

11. A decimal fraction may be written as a-frac¬ 
tion. .3 =_ 

12. .75 may be written as a common fraction with- 

for its numerator and_for its denominator. 

13. Per cents may be changed to-or-fractions. 

14. The whole of anything may be expressed as -- 

per cent. 















52 


THE BAYNE-SYLVESTER ARITHMETIC 


43. Percentage 

You have learned to express a part of a number as (1) a 
common fraction; (2) a decimal; (3) a per cent. For 
example, one fourth may be expressed as the common 
fraction or as the decimal fraction .25, or as 25%. 

‘‘Per cent’' means hy the hundred. The expression 
“per cent” is commonly used in business to denote hun¬ 
dredths, or hundredths times. The sign for per cent is %. 

1 . Read: 6% 1.5% 16f% 

35% 2.8% 121% 

125% 15.3% 8J% 

2. Write, using the per cent sign: one per cent; one 
hundred per cent; thirty-seven and one-half per cent. 

3. Write in decimal form: 15%, 7%, 7^%, 105% 

4 . Write as per cents, using the per cent sign: 


.07 

.18 

7 

5 

100 

100 

.161 

.01 

25 

33i 


100 

100 

6. Complete the following: 






eighteen 

Example: 18% 

18 per cent .18 


hundredths 

(a) 

9 per cent 



(6) 

(c) 

(<D 12i% 

(e) 

.075 

1 0% d 

five thou¬ 
sandths 

(/) 125% 

(g) 

ih) 1% 

.05 




SEVENTH GRADE 


53 


6. (a) 50% of $160 is the same as of $160. 

(b) .50 of $160 is the same as_% of $160. 

7 . (a) Write 75% as a common fraction. 

(b) 23% of a number is the same as_of the 

number. 

(c) Write 23% as a common fraction. 

(d) Write 16f% in five different ways. 

8. Write the fractional and decimal equivalents of each 
of the following per cents which are frequently used in 
business: 

Fractional Decimal Fractional Decimal 

Equivalent Equivalent Equivalent Equivalent 



50% 

25% 

75% 

10 % 

33i% 

12 |% 



44. Finding a Per Cent of a Number 


In a school with a register of 1800 boys, 35% were 
enrolled as members of the Boy Scouts. How many boys 
were members of the Boy Scouts? 


1800 boys 


35% = .35 
.35 of 1800 boys = 
.35 X 1800 boys 


.35 

9000 

5400 


630.00 boys were members 






54 


THE BAYNE-SYLVESTER ARITHMETIC 


Finding a per cent of a number is the same as multiply¬ 
ing the number by a decimal. 

Without pencil. 

1. Complete and solve: 

(a) 8% of S720 = .08 X_ 

(5) 12% of $960 = _X $960 

(c) 4% of $1528 - _X _ 

(d) 25% of $644 = .25 _ $644 

2. Our spelling test this morning consisted of 40 words. 
Annans rating was 90%. How many words did Anna 
spell correctly? 

3. On a stormy day the attendance record of a class of 

36 pupils showed that 25% of the pupils were absent. 
_pupils were absent; _pupils were present. 

4. Our team played 20 games this season. We lost 
10% of all the games played. How many games did we 
lose? 

5. A certain team played 40 games during the baseball 
season and won 80% of the games it played, (a) How 
many games did the team win? (b) How many games 
did it lose? 

6. Mary should weigh 120 lb. Her present weight is 
5% below the average, (a) How many pounds is she 
below the average weight? (b') What does she weigh at 
present? 

7. On September 9 there were 32 pupils on register in a 
7A class. During the month, this number was increased 
by 25%. How many new pupils were enrolled during 
the month? 










SEVENTH GRADE 


55 


Use pencil when needed. 

8. In a school of 2500 pupils, 98% joined the Red 
Cross, (a) How many joined the organization? (6) How 
many did not join? (c) What per cent did not join? 

9. During a school year of 190 days, Mary Murray 
attended 90% of the time. How many days did Mary 
attend school? 

10. Fred weighed 64 lb. in June. During the vacation 

period he gained 12^% in weight, (a) He gained- 

pounds, ih) Then he weighed_pounds. 

11. In a school of 1900 pupils, 92% were promoted at 

the end of the term. _pupils were promoted; - 

pupils were not promoted. 

12. In Jackson School, 85% of the boys have bank 

accounts. If there are 720 boys in the school,-boys 

are depositors in the school bank, and-boys have no 

accounts. 

With pencil. 

13. A man earns $6500 per year. He spends 30% of 
his income for rent. How much does he spend for rent? 

14. A library contains 1664 books. Of these, 12j% 

are reference books. There are_reference books in 

the library. 

15. A man saves 15% of his salary of $450 per month. 
How much money does he save each month? 

16. For our school entertainment we had 960 tickets 
printed. Of these, 95% were sold, (a) How many 
tickets were sold? ih) How many remained unsold? (c) 
If the tickets were sold at 5^ each, how much money was 
received? 



56 THE BAYNE-SYLVESTER ARITHMETIC 

17. There are 1260 girls in a junior high school. Of 

these, 33are in eighth-year classes. There are- 

girls in eighth-year classes. 

*18. A dealer bought goods for $1750 and sold them at 
45% profit, (a) What was the amount of his profit? 
How much did he receive for the goods? 

*19. A family having an income of $4000 per year spent 
25% for food, 20% for rent, 15% for operating expenses, 
and 20% for clothing. The remainder was used for in¬ 
surance and savings, (a) How much money was allowed 
for food? (h) For rent? (c) For operating expenses? 
(d) For clothing? (e) Y^Tiat per cent of the income was 
used for insurance and savings? 

20. A farmer raised 450 bu. of wheat and sold 75% of 
his crop. How many bushels of wheat did he sell? 

*21. In an orchard of 2400 trees, 25% were apple trees, 
15% were pear trees, and 37|% were cherry trees. The 
remainder were peach trees, (n) How many trees of each 
kind were planted in the orchard? (5) W^hat per cent of 
the trees were peach trees? 

45. Adding and Subtracting Per Cents 

You know that f equals one unit, or one. The same is 
true of f and of ^ and of ^ and of yV- 

of a number equals the number itself. Similarly, 
since 100% is the same as ^ of a number, 100% of a 
number equals the number itself. 

1. Complete the following: 

(a) 100% of $250 is_ (d) 100% of 3.6 is- 

(b) 100% of $75 is_ (e) 100% of .36 is- 

(c) 100% of 36 is_ (/) 100% of .036 is- 









SEVENTH GRADE 


57 


2. (a) 100% + 25% = ? (c) 100% - 25% = ? 

(5) 100% + 18% = ? (d) 100% - 46% = ? 

3. Class 7A had a midterm test in grammar, on which 
25% of the class were rated A, 35% were rated B, and 15% 
were rated C. The remainder of the class were rated D. 
What per cent of the class received a rating of D? 

*4. In a recent spelling test, 25% of a class of 40 pupils 
received a grade of 100, 40% received 95, and 15% re¬ 
ceived 90. The remainder of the class received grades 
between 85 and 90. Find the number of pupils in each 
group. How can you check your answers? 

5. A farmer had 160 A. of land under cultivation, of 
which 40% was planted in rye, 25% was planted in wheat, 
and the remainder was planted in corn. How many acres 
were planted in corn? 

6. By the terms of a man’s will, his estate of $24,000 
was divided among his two daughters and a son. Each 
daughter received 35% of the estate. The remainder was 
left to the son. (a) What per cent of the estate did the 
son receive? (6) How much money did each child 
receive? 

7. At different times, Mr. Atkins sold 35%, 18%, and 
20% of his crop of potatoes, (a) What per cent of his 
entire crop did he sell? (b) What per cent had he left? 

46. Per Cents More Than 100 

There are 40 pupils in a seventh-grade class. If 100% 
are present, how many pupils are present? 

100% of a number = the number itself. 

Therefore, 40 pupils were present. 




58 


THE BAYNE-SYLVESTER ARITHMETIC 


In 1900 the number of voters in a certain town was 320. 
In 1929, the number of voters was 200% of what it was in 
1900. How many voters were there in 1929? 


200 % = = 2 

There were twice as many voters in 1929 as in 1900. 
2 X 320 = 640 voters in 1929 


1. Complete: (a) 500% = = 5 

{h) ? = ^ 

(c) 900% = = 9 

id) 700% = = ? 

2. What number is 300% of 75? 

3. Because of an increase in population in the town of 
Newton, the receipts of the Union Gas Company in that 
town are 300% as great now as they were ten years ago. 
How many times as great are the receipts today? 

Last year James Burton earned $600. This year his 
earnings are 125% of what they were last year. What 
are his earnings this year? 


A. 125% = iM = f 

125% — — 1.25 

5 $150 


1 X $750 

1.25 X $600 = $750 


4, Complete the following: 

(a) 125% of 560 =_X 560 

(b) 150% of 880 =_X 880 







SEVENTH GRADE 


59 


(c) 225% of 1284 = _X_ 

(d) 340% of 520 =_X_ 

{e) 133i% of 426 = _X_ 

(/) 116f% of 906 =_X_ 

5. Find: (a) 312^%of $324.40 
(h) 125% of $248 

(c) 175% of $24.72 

(d) 275 % of $48.60 

47. Short Ways of Finding Per Cent 

Fred is bank manager of his class. He reports that, 
of 40 boys in his class, 10% have no bank accounts at 
present. How many boys are without accounts? 


19% — .10 — — Y^ 

yV of 40 boys = 4 boys 


In a class of 36 pupils, 25% had perfect attendance for 
the month of May. How many pupils had perfect 
attendance? 


A. Per cent changed to 

B. Per cent changed to 

decimal equivalent 

fractional equivalent 

25% = .25 


36 


.25 

180 

1 9 

j X -36^ 9 pupils 

72 

9.00 pupils 





60 


THE BAYNE-SYLVESTER ARITHMETIC 


To find a per cent of a number, change the per 
cent to its fractional or decimal equivalent and then 
multiply. 


Which method is shorter? Which do you prefer to use? 

Change the following per cents to common fractions and 
solve: 

1 . 


2 . 

3. 

4. 


25 % of S3.28 

(e) 

12|% of $9.60 

50 % of 112.60 

(/) 

37i% of 48.8 

75 % of 3.6 

{g) 

40 % of $3.20 

66f% of 4.8 

(h) 

33i% of $96.30 


{%) 62of $1.44 

(a) 87^% of 43.2 = (c) 70 % of 28.56 = 

ib) 66f% of 1546 = (d) 16|% of 72.06 = 

What number is 20% of 25? Of 35? Of 60? 

Miss Slater gave 12 examples as a test in percentage. 
John’s paper was graded 75%. How many examples did 
he work correctly? 

5. George had 60^ this morning. He spent 40% of it 
for stationery. How much did he spend? 

6. A man earns $750 per month. If his salary is in¬ 
creased 20%, how mucn more money will he earn per 
month? 

7. A farmer raised 2730 bu. of wheat. He sold 33|% 
of his crop to a neighbor. How many bushels did he sell? 

8. A real-estate dealer bought a lot for $1280. He sold 

it at a gain of 12|%. (a) How much money did he gain? 

(6) How much did he receive for the lot? 



SEVENTH GRADE 


61 


48. Finding What Per Cent One Number Is of Another 

A grocer had 60 lb. of coffee on hand. He sold 30 lb. 
(a) What part of his stock did he sell? {h) What per 
cent of his stock did he sell? 


A. 

B. 

60 lb. = total stock 

60 lb. = 100% of stock 

‘RO IK ^ 1 

60 6 2 


The grocer sold \ of his 

The grocer sold 50% of his 

stock of coffee. 

stock of coffee. 


Fred had $.64. He spent $.40 for 
his lunch. What per cent of his 
money did he spend for lunch? 


= 62 i% 


Can you prove the answer to this example? How 
would you do so? 

Mother had a bag of sugar weighing 25 lb. She used 
19 lb. in making jelly. What per cent of the 25 lb. did 
she use? 


^ of the sugar was used. 

.76 .76 = 76% 

Check: 25 

25)19.00 

.76 

17 5 

150 

1 50 

175 

1 50 

19.00 76% of 25 lb. 

= 19 lb. 










62 


THE BAYNE-SYLVESTER ARITHMETIC 


To find what per cent one number is of another, 
first find what fractional part it is. Then change 
the common fraction to a decimal and the decimal 
to a per cent. 


(a) (h) 

1 . 

2 . 

3. 

4. 

6 . 

6 . 

7. 


12 is what part of 36? 

12 is what part of 8? 

30 is what part of 90? 

12 is what per cent of 18? 
8 is what per cent of 24? 

100 is_% of 20. 

36 is_% of 24. 


What per cent of 36? 
What per cent of 8? 

What per cent of 90? 

25 is what per cent of 15? 
60 is what per cent of 48? 

30 is_% of 100. 

16 is_% of 12. 


* An article which cost $.24 was sold for $.36. What 
was the per cent increase in price? 


$.36 — $.24 = $.12 increase in price 
^ = 1 = .50 = 50% increase in price 


* 8 . A book which cost $.48 was sold for $.60. What 
was the per cent increase in price? 

*9. Find the per cent increase in price for the following: 
Cost Selling Price Cost Selling Price 

(a) $.36 $.40 (c) $5.00 $5.50 

(5) $.18 $.27 (d) $.72 $.80 








SEVENTH GRADE 


63 


49. Problems in Percentage 

Without pencil. 

1 . If Charles works 8 out of 10 examples correctly, 

his paper should be marked_%. 

2. A spelling test contained 12 words. Jane mis¬ 
spelled 4. What per cent of the words in the test did she 
misspell? 

3. Of a total of 15 examples in decimals, Fred worked 
12 correctly. What per cent of the examples did he work 
correctly? 

4. A boy had $.50. He spent $.20 for school supplies 
and the remainder of his money for lunch. What per 
cent of his money did he spend for his lunch? 

5. (a) What per cent of 25 is 20? (6) 15 is what per 

cent of 20? 

Use pencil if needed. 

*6. An article which cost $4.50 was sold for $6.30. 
What was the per cent of gain? 

7. Mr. Brown’s income is $7500 per year. If he 
pays $1800 per year for rent, (a) what fractional part of 
his income does he spend for rent? (6) What per cent of 
his income does he spend for rent? (c) What amount of 
rent does he pay per month? 

8. A merchant sold at $72 each coats which cost him 
$54 each. What per cent did he gain on each coat? 

9. Out of 120 times at bat, a player made 45 hits. 
What was his batting average? 

10. In a certain number of games, a left fielder ac¬ 
cepted 32 chances out of 36. What per cent of chances 
did he accept? 


64 


THE BAYNE-SYLVESTER ARITHMETIC 


11. A club grew in membership from 180 to 200. 
What was the per cent of gain in membership? 

*12. Another club decreased in membership from 360 
to 315. What was the per cent of loss in membership? 

13. On a salary of $1800 per year, Fred White saves 
$360. What per cent of his salary does he save? 

14. A farm of 320 A. has 120 A. in pasture. What 
per cent of the farm is in pasture? 

15. Mr. Chase’s salary was $2400. If it was increased 
to $2616, what was the per cent of increase? 

16. Class 7A has a register of 45 pupils. Last week, 
the following numbers of pupils passed morning inspec¬ 
tion: Monday, 36; Tuesday, 40; Wednesday, 42; Thurs¬ 
day, 35; Friday, 45. What per cent of the class passed 
morning inspection on each of the five days? 

*17. In 1925 the population of a town was 8050. In 
1929 it was 6440. What was the per cent of decrease in 
population between 1925 and 1929? 

18. A newsboy sold 108 of his 120 papers. What per 
cent of his papers did he sell? 

19. In September a class register was 45 pupils; in 
June it was 54 pupils. What was the per cent of increase? 

60. Finding a Number When a Per Cent Is Given 

If 4 pairs of gloves cost $6.00, what will 5 pairs cost? 


4 pairs cost $6.00 

1 pair costs i of $6.00, or $1.50 

5 pairs cost 5 X $1.50, or $7.50 




SEVENTH GRADE 65 

If f of a sum of money equals 16.00, what is the entire 
sum of money? 

4 

■= of the money = $6.00 
o 

1 1 $1.50 

g of the money = | X ,S&rO<r = $1.50 

-= of the money = 5 X $1.50 = $7.50 
o 

4 $1.50 

Check: | X S6.00 


If 80% of a sum of money equals $6.00, what is the 
entire sum of money? 


A. 80% = .80 = = I 

f of the sum = $6.00 
^ of the sum = | X $6.00 = $1.50 
I of the sum = 5 X $1.50 = $7.50 
. $1.50 

Check: ^ X $6.00 

5 


B. 80% = .80 = xW 

of the sum = $6.00 
of the sum = ^ X $6.00 = $.075 
of the sum = 100 X $.075 = $7.50 
Check: 80% of $7.50 = $6.00 






66 


THE BAYNE-SYLVESTER ARITHMETIC 


To find a number when a per cent is given: 
(1) change the per cent to a common fraction and 
solve; or (2) find 1% of the number given and 
then multiply 1% of the number by 100 to obtain 
100% of the number. 


Use 'pencil when needed. 


Complete the following: 


1. (a) 

25% of ? 

= 18 

id) 

16f% of ? 

= $3.60 

(b) 

10% of ? 

= $1.75 

ie) 

66f% of ? 

= $1.44 

(c) 

50% of ? 

= $.96 

if) 

87i% of ? 

= $12.60 

2. (a) 

720 bu. = 

80% of 

? 

(c) $6.48 = 

37i% of ? 

(b) 

85 bu. = 

62i% of 

? 

(d) 3960 = 

75 % of ? 


51. Problem Review 

Without pencil. 

1. Mary had $.40 in her purse. This was 25% of 
what Jane had. How much money had Jane? 

2. Frances spent $1.50 for a pair of gloves. This 

was 50% of the amount of money which Uncle Frank had 
given her as a birthday gift. Uncle Frank gave Frances 
$_ 

3. $21 is what per cent of $84? 

4. A school term won 5 games out of the 8 it played. 

The team won_% of the games it played. 

5. A dealer bought balls at $.25 each and sold them 
for $.30 each. What per cent of the cost did he gain? 

*6. A book that cost $2.50 was sold for $2.00. What 
was the per cent of loss? 





SEVENTH GRADE 


67 


With 'pencil, 

7. If 9% of a number is 135, what is the number? 

8. Find the number of which 210 is 7%. 

9. If 12% of a number is 240, what is the number? 

10. $17 is 25% of $_ 

11. What is the cost of a plot of ground if 15% of the 
cost is $300? 

12. $210 is what part»of $240? 

*13. Mr. Stevens bought a piano for $750. He paid 
$450 to the dealer at the time of purchase, (a) What 
per cent of the purchase price did he pay? (6) How much 
money was still due? (c) What per cent of the purchase 
price was still due? 

14. If 18% of the number of girls in the Bryant School 
is 556, how many girls are there in the school? 

15. 434 is 63% of_ 

16. If $85 is 62|% of the cost of a sofa, what is the 
cost of the sofa? 

17. A salesman is obliged to travel 360 mi. from one 
city to another. After he has traveled 270 mi., what 
per cent of the total distance has he still to travel? 

*18. A house that cost $5000 was sold for $4750. Find 
the per cent of loss. 

19. Jane received $15 as a birthday gift. She spent 
$7.50 for shoes and $5.00 for a new hat. (a) What per 
cent of the $15 was spent for the shoes? (5) For the hat? 
(c) How much money was left? (d) What per cent of 
the $15 was left? 

20. The weekly salaries of certain clerks in the Boston 
Store for two years were as follows. Find the per cent of 
increase or decrease in salary in each case: 



68 

THE 

BAYNE-SYLVESTER 

ARITHMETIC 


First 

Second 


First 

Second 

Clerk 

Year 

- Year 

Clerk 

Year 

Year 

A 

$16 

$18 

F 

$7.50 

$10.00 

B 

$25 

$30 

G 

$22.50 

$25.00 

C 

$35 

$30 

H 

$12.50 

$10.00 

D 

$45 

$55 

I 

$20.00 

$40.00 

E 

$25 

$24 

J 

$15.00 

$20.00 


52. Completion Exercise 

Fill in blank spaces with reasonable numbers. Then solve 
each problem : 

1 . The Johnsons lived in an apartment on M Street 

from January 1 to September 30 and paid a monthly 
rental of S75. On October 1 they moved into a new apart¬ 
ment on J Street, paying _% more rent per month. 

What was their average rent per month for the year? 

2. An article bought for $_ was sold for $ - 

What was the per cent of gain? 

3. Edward earned $18 a week and saved $_each 

week. What per cent of his salary did he save? 

4. John earns $22 per week and saves __% of it. 

How much money does he save each week? 

5. The population of a certain town was 14,500 in 

1919. Ten years later it had increased by_%. What 

was the population of the town in 1929? 

6. An article which cost $8.50 was sold at a loss of 
_%. For what price was the article sold? 

7. Mr. Charleton drove his automobile 191.25 mi. in 
7.5 hr. What was his average speed per hour? 

8. At another time Mr. Charleton drove for 6.25 hr. 
at the rate of 21.3 mi. per hour. How many miles did he 
cover? 



SEVENTH GRADE 


69 


63. Per Cents Less Than One Per Cent 

Mr. Frazer sold $3600 worth of merchandise at 
commission. How much money did he receive? 


1% of $3600 = $36.00 of $3600 = i of $36 = $18 


Occasionally you will be called upon to deal with per 
cents less than 1%. These small per cents will cause 
trouble and confusion unless you are careful. 

What is i% of 848? 

Think: 1% of 848 = 8.48 

1 2.12 

i% of 848 = j 2.1^ 


1 . Find: 

(a) of 96 (d) i% of 753 

(b) i% of 728 (e) i% of 1250 

(c) i%of$262 (/) i%ofl44 

*At f % commission, what will an agent receive on sales 
amounting to $4880? 


Think: 1% of $4880 = $48.80 

$12 20 

f% of 14880 = I X = 136.60 





70 


THE BAYNE-SYLVESTER ARITHMETIC 


2. Find: 

(а) 1% of 968- 

(б) |%ofS780 
(c) 1% of 655 
id) \% of 144 


(e) 1% of 5280 
(/) of 12550 
{g) 1% of 1720 
(A) of S960 


3. At f% commission, what will an agent receive on 
sales amounting to $6930? 

4. A commission merchant charges %% for his ser¬ 
vices. What will be his commission if he sells $7200 worth 
of goods? 

6. The United States levies a tax of on certain 
classes of income. At this rate, what would be the 
amount of the tax on $300? 

6. The commission on sales amounting to $540, at 

i%, is-• 


64. Sentences for Completion 


Complete the following sentences: 


1. To find 12% of a number, we _ the number 

by- 

2. 12% of $200 is .12 X_ 

3. 25% of 24 is_X_ 

4. 18 is_% of 24. 

5. If 16 is 25% of a number, the number is- 

6. 16 is 50% of_ 

7. 12j% = the common fraction_ 



_% of this rectangle 

is shaded. 



_% of this rectangle 

is unshaded. 





















SEVENTH GRADE 


71 


9. ^ of a number equals_% of the number. 

10. (a) One way of finding 37|% of a number is to_ 

the number by_ 

(b) Another way to find 37^% of a number is to 
find_of the number. 

11. .35 of a number is the same as _% of the 

number. 

12. .625 is the same as_%. 

13. 50% of a number is just_as large as the number 

itself. 

*14. 25% of 36 is just half as much as_% of 36. 

15. Written as a common fraction, 45% would have 

_as its numerator and_as its de¬ 
nominator. 

16. Each portion of this circle represents 
_% of the circle. 

17. This tumbler appears to be about_ 

full of water. 

18. _% of a number equals 

the number itself. 

19. _% of this square has been left 

unshaded. 

20. _% of this square has been shaded. 

21. Draw a line 6 in. long. A line 50% 

as long will measure_in. 

22. Draw a rectangle. Shade 75% of it. 

23. Draw a circle. Shade 75% of it. 





























72 


THE BAYNE-SYLVESTER ARITHMETIC 


55. Estimating 

1. 23% of any number is nearly 25% of the number, 
or about \ of the number. 

2. 23% of 48 is about- 

3. 52% of a number is nearly ] of the number. 

4. 73% of a number is nearly I of the number. 

5. 48% of $30 is about $- 

6. 22% of $120 is about i of $120, or $- 

7. 52% of $120 is about ? of $120, or $- 

8. Is 73% of $120 more or less than f of $120? Why? 

9. 32% of a number is nearly f of the number. 

10. 32% of $60 is about $- 

11 . Is 65% of $96 more or less than f of $96? Can 
you prove your answer? 


56. Review of Percentage 


Complete the following: 


( 0 ) 

50% 

of 126 = . 


(b) 

25% 

of 240 = . 


(c) 

20% 

of 160 = . 


id) 

12|% of 248 = 

— 

(a) 

63 is 

-%0f 

126 

(6) 

80 is 

-%of 

640 

(c) 

64 is 

-%0f 

320 

id) 

93 is 

-%of 

744 

(a) 

63 is 

50% of _ 


(b) 

64 is 

25% of _ 


ic) 

97 is 

20% of _ 


id) 

75 is 

121% of . 



(e) 33i% of 369 = _ 

(/) 371 % of 56 = - 

(g) 66f% of 189 = - 

(h) 40% of 800 = - 

(e) 369 is_% of 1107 

(/) 84 is_% of 224 

(g) 504 is_% of 756 

(h) 320 is_% of 800 

(e) 35is33|%of _ 

(/) 96 is 371 % of - 

(g) 144 is 66f% of - 

(h) 320 is 40% of _ 


SEVENTH GRADE 


73 


67. Percentage Race 

Compete row against row. Work quickly but accu¬ 
rately. 

Work for 30 minutes. Find the average number right 
for each row. The row with the highest average wins. 


A 

1 . 12% of 11800 = ? 

2. 4i% of 625 = ? 

3. ? ft. = 875% of a mile. 

4. What is 125% of 1600? 

6. What per cent of 24 is 18? 

6. 1760 ft. = ? % of a mile. 

7. 62i% of ? = $75. 

8. ? = 8i% of 600. 

9. Find 18% of $2400. 

10. 45 min. = ? % of an hour. 

11. What is 37i% of 1760 yd.? 

12. $800 + 4% of $800 = ? 

13. 250 lb. = ? % of a ton. 

14. 5|% of 725 = ? 

16. ? = 4% of 375 yd. 

16. 75 = ? % of 150. 

17. 200% of 1 mile = ? ft. 

18. 66|% of ? = $900. 

19. What per cent of 15 is 9? 

20. 37i% of ? = 240. 

21. 225% of 1500 = ? 

22. ? % of 72 is 64. 

23. $1200-25% of $1200= ? 

24. 621% of ? = 750. 

26. 24 in. = ? % of a yard. 


B 

Find 62i% of 6456. 

? = 5|% of 850. 

75% of $25,000 = ? 

$50 = ? % of $300. 

125 % of 1 yd. = ? in. 

250% of $3600 = ? 

125 = ? % of 500. 

1200 = 80% of ? 

2400 - 15% of 2400 = ? 
li% of $1000 = ? 

What is 8 % of 750 ft.? 

1 pint = ? % of a gallon. 

? = 175% of 850. 

112i% of 6372 = ? 

? % of 1200 is 400. 

$1800 + 200 % of $1800 = ? 
15% of 382 = ? 

What per cent of 50 is 48? 
375 ft. = 60% of ? 

8650 + 80% of 8650 = ? 

240 = 33i% of ? 

$1800 - 33i% of $1800 = ? 
What per cent of 1 sq. ft. = 
72 sq. in.? 

375 = 60% of ? 

300% of $75 = ? 


74 


THE BAYNE-SYLVESTER ARITHMETIC 


68. Step-by-Step Test Drill — Percentage 



A 

B 

c 

D 

E 

1. 

6% of 
5286 = 

4% of 
8927 = 

7% of 
6852 = 

8% of 
9269 = 

5% of 
6728 = 

2. 

15% of 
$607.25 = 

82% of 
$930.74 = 

48% of 
$605.43 = 

56% of 
$820.96 = 

38% of 
$904.56 = 

3. 

4}% of 
8265 = 

5i% of 
16"00 = 

3i% of 
9260 = 

8f % of 
6400 = 

4i % of 
8640 = 

4. 

500% of 
2693 = 

300% of 
8496 = 

200% of 
8375 = 

600% of 
2987 = 

800% of 
8462 = 

5. 

87§% of 
$20,56 = 

66f% of 
$64.50 = 

80% of 
$81.60 = 

83i% of 
$68.22 = 

60% of 
$29.85 = 

6. 

150% of 
2846 = 

125% of 
8268 = 

275% of 
3740 = 

133i% of 
6075 = 

112i% of 
5648 = 

7 . 

115% of 
$54.42 = 

137% of 
$1800 = 

164% of 
$2400 = 

218% of 
6250 = 

142% of 
8450 = 

8. 

-- 25 - — • /O 

fi= ?% 

If = ? % 

JL 7-5 oy 

112 = ^ or 

10 0- /o 

9. 

300 = ? % 
of 500 

175 = ? % 
of 350 

75 = ? % 
of 175 

84 is ? % 
of 100 

65 is ? % 
of 150 

10. 

1% of ? 

= 325 

10% of ? 

= 450 

20% of ? 

= 625 

8§% of ? 

= 8648 

16f% of ? 

= 1500 

11. 

37i% of ? 
= $32.40 

40% of ? 

= $86.50 

62i% of ? 
= $82.30 

75% of ? 

= $27.24 

70% of ? 

= $49.56 































SEVENTH GRADE 


75 


59. Finding a Part of a Number 

Mr. Brown earns $2400 a year, (a) If he spends f of 
his salary, how much does he spend? (b) If he spends 
.75 of his salary, how much does he spend? (c) If he 
spends 75% of his salary, how much does he spend? 


A. 

4 of his salary = 
$2400 

i of $2400 = $600 
|=3X$600 = $1800 
He spent $1800. 


B. 

.75 = I 

O $600 

I X S2mr= $1800 
He spent $1800. 


C. 

75% = .75 = f 

O $600 

j X $2400^= $1800 
He spent $1800. 


When a decimal or per cent in a problem can be 
changed to a common business fraction, change it 
to the fraction and use the fraction in finding the 
part of the number. 


Problem C is called the first case in percentage. 


Find: 


(a) 


1 . 

2 . 

3. 

4. 

5. 

6 . 

7. 

8 . 


f of 56.63 
I of 55.80 
^ of 144.72 
I of 43.80 
I of 67.20 


(b) 

.75 of $6400 
.875 of 7256 lb. 
.83| of S30.54 


(c) 

25% of 18,246 
50% of 62,980 
62i% of 83,246 
16f% of 54,936 
33^% of 82,965 


.375 of 3680 ft. 

How many feet are there in .375 of a mile? 

How many square inches are there in .75 sq. ft.? 
How many square feet are there in .50 sq. yd.? 






76 THE BAYNE-SYLVESTER ARITHMETIC 

9 . How many pounds are there in .25 of a ton? 

10. Whatis66 f%of 3672 bu.? 

11 . A house bought for $16,000 was sold at a gain of 
12^%. What was the selling price? 

12 . The distance by automobile between Rockland and 
Portland is 84.8 mi. When Fred had traveled 75% of the 
distance, a tire blew out. How many miles remained to 
be traveled? 

13. A man with an annual income of $3600 saves 20% 
of it. How much does he save? 

60. Finding What Part One Number Is of Another 

A farmer raised 1500 bu. of wheat. He sold 1000 bu. 
(a) ^Yhat part of his crop did he sell? (b) How many 
hundredths of his crop did he sell? (c) What per cent 
of his crop did he sell? 


A. 

B. 

C. 

1 0 0 0 _ 2 

3 

1 0 0 0 _ 2 

15 0 0 3 

1 0 0 0 _ 2 

1^0 0 3 

He sold f of his 

i = .661 

I = .661 = 66f% 

crop. 

He sold .66f of 

He sold 66f % of 


his crop. 

his crop. 


To find what part one number is of another, 
express the relationship as a common fraction in 
its lowest terms, using as the denominator the 
number of which the part is taken. 

To find what per cent one number is of another, 
reduce the fraction to its decimal equivalent and 
then to a per cent. 






SEVENTH GRADE 


77 


Problem C is called the second case in percentage. 

Complete the following by supplying in (a) the missing 
fractional part; in (b) the missing decimal part; and in (c) 
the missing per cent: 


(a) (6) 

1. 800 is ? of 3000 86 is ? of 150 

2. ? of 2500 is 1800 ? of 75 is 30 

3. ? of 2600 is 1300 21 is ? of 84 

4. 250 is ? of 3250 86 is ? of 172 

5. 300 is ? of 1800 ? of 78 is 39 

6. 146 is ? of 150 ? of 75 is 20 

7. What decimal part of 48 is 24? 

8. What decimal part of 177 is 59? 

9. What decimal part of 96 is 32? 

10 . What decimal part of 75 is 15? 


(c) 


20 is ? 

of 

125 

60 is ? 

of 

160 

? of 45 

is 

30 

? of 64 

is 

16 

45 is ? 

of 

75 

58 is ? 

of 

464 


Complete the following: 


11. 

800 is ? 

% of 600 

12. 

900 is ? 

% of 400 

13. 

1200 is 

? % of 400 

14. 

1600 is 

? % of 800 

15. 

1500 is 

? % of 1200 


16. 

$500 is 

? % of $1000 

17. 

12500 is ? % of S250 

18. 

$700 is 

? % of $350 

19. 

$150 is 

? % of $100 

20. 

$75 is ? 

% of $60 


61. Problems 

1. One pint is what per cent of a gallon? 

2. One inch is what per cent of a foot? 

3. Mr. Abbot ordered 12 T. of coal for the winter. 

After two months he had used 4 T. What per cent of the 

coal had he used? 

4. The following table shows the price per ton of hard 
and soft coal from 1900 to 1925: 


78 


THE BAYNE-SYLVESTER ARITHMETIC 


Year Hard Coal 

1900 $4.26 

1905 $4.99 

1910 $4.94 


Soft Coal Year 

$2.26 1915 

$2.63 1920 

$2.49 1925 


Hard Coal Soft Coal 

$5.27 $2.53 

$9.44 $8.85 

$11.19 $4.39 


(a) Find the difference between the 1900 and 1925 prices 
of hard coal. What was the per cent of increase? (Two 
decimal places.) 

(b) Find the difference between the 1900 and 1925 
prices of soft coal. What was the per cent of increase? 
(Two places.) 

(c) Which kind of coal shows the greater per cent of 
increase? How much greater is it? 

5 . Compare the 1900 with the 1920 prices. Which 
kind of coal showed the greater per cent of increase? How 
much greater was it? 

6 . Make up a problem in percentage using the informa¬ 
tion in the table. 


62. Finding a Number When a Part Is Given 

Sarah saves $4 each week. How much does she earn 
if this is (a) f of what she earns; (6) .4 of what she earns; 
(c) 40% of what she earns? 


A. 


f of her earnings = $4 
i = $4-^2or iof S4 = $2 
|.==5x$2 = $10 


B. Change .4 to f and solve 
as in d. 

C. Change 40% to f and 
solve as in d. 


Problem C is called the third case in percentage. 





SEVENTH GRADE 


79 


Find the number of which 



(a) 

(b) 

(c) 

1 . 

18 is I 

24 is .2 

39 is 60% 

2 . 

25 is f 

75 is .375 

129 is 66 f% 

3. 

600 is 1 

120 is .75 

650 is 62|% 

4. 

2400 is I 

150 is . 66 f 

910 is 70% 

5. 

1800 is f 

721 is .87| 

570 is 30% 

6 . 

Mr. Wright sold 322 bu. of wheat. 

This was 33 5 % 


of his crop. How many bushels did he raise? 

7. Forty-two children in a class were promoted. This 
was 87of the register. What was the register? 

8 . Mr. Ward drove his automobile 120 mi. one day. 
This was 40% of the distance he planned to go. How 
many miles did he intend to travel? 

9. Mr. Bates sold 350 bu. of potatoes. This was 
83^% of his crop. What did his crop amount to? 

10 . Mrs. Reed saves $1500 a year. This is 37|% of 
her income. What is her income? 

11 . A man rented a house for $900 a year. This 
amounted to .15 of the cost of the house. What did the 
house cost? 

12 . Mr. Willis sold an automobile for $1800. This 
was 66 1% of the cost. What was the cost of the car? 

63. Reduction of Denominate Numbers 

Denominate numbers expressed in different units must 
be changed to the same unit before a problem can be solved. 
Sometimes they must be reduced to a higher unit, some¬ 
times to a lower unit, and sometimes to a fractional part 
of a larger unit. 


80 


THE BAYNE-SYLVESTER ARITHMETIC 


Fred’s height is 58 in. Express his height in feet and 
inches. 


I ft. = 12 in. 58 in. -f- 12 = 4 ft. 10 in. 


Find the cost of 5 yd. 2 ft. of fence wire @ S.15 a foot. 


5 yd. = 5 X 3 ft. = 15 ft. 15 ft. + 2 ft. = 17 ft. 
17 X $.15 = $2.55 


Find the area of a plot of ground 12 ft. wide and 18 ft. 
8 in. long. 


18 ft. 8 in. = 18i ft. 12 ft. X 18f ft. = 224 sq. ft. 


1. 

9 ft. 7 in. 

= in. 

14. 

32 in. = yd. 

2. 

min. 

= 1 hr. 45 min. 

15. 

27 in. = yd. 

3. 

oz. = 

1 lb. 4 oz. 

16. 

1 yr. 8 mo. = yr. 

4. 

1 doz.+5 

= units 

17. 

2 yr. 6 mo. = yr. 

6. 

24i hr. = _ 

min. 

18. 

3 vr. 4 mo. = yr. 

6. 

1^ mi. = 

ft. 

19. 

45 min. = hr. 

7. 

80 min. = 

hr. min. 

20. 

24 hr. = min 

8. 

75 in. = 

ft. in. 

21. 

1 yr. 8 mo. = mo. 

9. 

16 wk. = 

mo. 

22. 

96 hr. = da. 

10. 

24 mo. = 

yr. 

23. 

27 sq. ft. = sq. yd. 

11. 

20 dimes = 

= $ 

24. 

104 wk. = da. 

12. 

55 pt. = 

qt. 

25. 

5 yd. 18 in. = yd. 

13. 

54 in. = 

- yd. 

26. 

1 yr. 2 mo. = yr. 

































SEVENTH GRADE 


81 


64. Liquid Measure 

4 gi. = 1 pt. 

2 pt. = 1 qt. 

4 qt. = 1 gal. 

How much milk do you drink each day? 

Gasoline is sold by the_ 

We generally buy cream in J_bottles. 

Supply the missing numbers: 

1. 8 gal. =_pt. 4. 14 qt. = _gal. 

2. _pt. = 4 qt. 5. 9 pt. = _qt. 

3. 1 qt. = _gi. 6. _gal. = 17 qt. 

Use pencil if needed. 

7 . Harold had a lemonade stand at the fair. He made 
3 gal. for 30^ a gallon. He sold it in half-pint glasses at 
5^ a glass. What was his profit? 

8. How many half-pint bottles of cream can be filled 
from a 2-quart can? 

9. At 9^^ a pint, what will a gallon cost? 

10. Mrs. Jones uses 2 qt. of milk daily. How many 
gallons does she use in a week? 

11. Miss Stevens ordered 64 half-pint bottles of milk 
for the pupils in her class. How many quarts did this 
equal? 

12. Mrs. Walters orders a quart of milk a day for each 
of her two children and a pint for each of the three adults 
in the family. How many quarts are used in this family 
each day? 

13. At 28^ a half-pint, what will a quart of cream cost? 




82 


THE BAYNE-SYLVESTER ARITHMETIC 


66. Linear Measure 

12 in. = 1 ft. 

3 ft. =1 yd. 

5K yd. or 161^ ft. = 1 rd. 

320 rd. or 5280 ft. = 1 mi. 

Which unit would you probably use in measuring the 
length of your room? The height of the pupils? A 
length of dress goods? The distance you live from school? 
Supply the missing numbers: 


1. 

rd. 

= 3 mi. 

5. ^ mi. = 

ft. 

2. 

rd. 

= i mi. 

6. J mi. = 

rd. 

3. 

2 rd. = . 

ft. 

7. 54 in. = 

yd. 

4. 

2 rd. = . 

yd. 

8. ft. = 

8 ft. 10 in. 


Use pencil if needed. 

9. The baseball diamond is 90 ft. on one side. How 
many yards does a boy run who makes a home run? 

10. Silk was offered for sale in different widths. Alice 
bought a yard of 27-inch material. Grace bought a yard 
of 32-inch material. Which had more silk? 

11. Who is taller: Fred, who measures 64 in., or 
Walter, who measures 5 ft. 6 in.? How much taller is he? 

12. Mary crocheted 90 in. of edging for a scarf. How 
many yards did she crochet? 

13. Henry can jump 5 ft. 10 in. in the standing broad 
jump. What is this distance in inches? 

14. How many feet deep is water when soundings show 
a depth of 150 fathoms? (1 fathom = 6 ft.) 

15. A steamer averages 22 knots an hour. How many 
miles is this? (1 knot = 1.15 mi.) 










SEVENTH GRADE 


83 


66. Measures of Time 


60 sec. = 1 min, 
60 min. = 1 hr. 
24 hr. = 1 da. 

7 da. =1 wk. 


4 wk. = 1 mo. 

12 mo. = 1 yr. 

100 yr. = 1 century 
365 da. = 1 common year 


366 da. = 1 leap year 


Leap years are the years which can be divided by 4 
without a remainder, except the century years. Century 
years are leap years if they can be divided by 400 without 
a remainder. 

Is 1930 a leap year? Why? 

When will the next leap year come? 

Without 'pencil. 

1. John reached the station at 12.35 to get a 12.20 
train. How many minutes late was he? 

2. Jane was in the movies for 90 min. How many 
hours was she there? 

3. How many days are there between Lincoln’s and 
Washington’s birthdays? 

4. A 5-hour school day will mean_minutes a day 

and_minutes a week. 

5. Anna sleeps 8 hr. a day. What part of a day does 
she sleep? 

6. A commuter spends 45 min. on the train morning 
and evening. How many hours is he on the train (a) 
each day? (5) Each week? 

7. Mrs. Franklin borrowed $2000 on May 1 and paid 
it back on September 1. What was the interest period? 




84 


THE BAYNE-SYLVESTER ARITHMETIC 


67. Square Measure 

144 sq. in. = 1 sq. ft. 

9 sq. ft. = 1 sq. yd. 

303^ sq. yd. = 1 sq. rd. 

160 sq. rd. = 1 A. 

What unit would you use in estimating the floor space 
of the classroom? The amount of floor space covered by 
a rug? The size of a farm? 


Without pencil. 

Supply the missing numbers: 


1. I A.= 

. sq. rd. 

4. i sq. yd. = 

sq. ft. 

2. 3 A. = 

sq. rd. 

5. 2 sq. ft. = 

sq. in. 

3. 3 sq. rd. = 

sq. yd. 

6. 72 sq. in. = 

sq. ft. 

With pencil. 




7. (a) How many square feet of blackboard are there 


in your classroom? (b) What would be its cost at 28^2^ a 
square foot? 

8. (a) What is the amount of floor space in your class¬ 
room? (b) Divide by the register of your class and find 
how much is allowed for each pupil. 

9. Some boys at play broke a window with a baseball. 
They offered to pay for the damages. What must they 
pay for a piece of glass 3 ft. by 4 ft. at 15^ a square foot? 

10. Mrs. Daniels bought a rug 9 ft. by 12 ft. to cover a 
floor 12 ft. by 15 ft. How many square feet of floor 
remained uncovered? 

11. The entry to a house measures 5 ft. by 4 ft. Which 
of these rugs will fit: a rug 6 ft. by 5 ft. or a rug 4j ft. by 

ft.? 








SEVENTH GRADE 


85 


68. Measures of Weight 

16 oz. = 1 lb. 

100 lb. = 1 cwt. 

2000 lb. = 1 T. 

Without pencil. 

1. Coal is supplied by the_or_ 

2. My weight is measured in_and_ 

3. Butter, tea, coffee, etc., are measured by the_ 

or_ 

4. How many ounces are there in 2f lb.? 

6. Find the cost of 1 lb. of sugar at $25 per hundred¬ 
weight. 

6. What will 1 lb. of a commodity cost if 100 lb. 
cost $7.50? 

7. The capacity of a freight car is 36,000 lb. What is 
the capacity in tons? 

8. A notice on a bridge reads, Limit, 8 tons.’’ What 
is the limit in pounds? 

Use pencil if needed. 

9. What is the cost of f lb. cinnamon at 10^ an ounce? 

10. At 4 oz. for 15^, what will lb. of peanuts cost? 

11. How many 8-ounce boxes can be filled from a bag 
of candy that contains 5| lb.? 

12. A dealer buys coal at $12 a ton and sells it for $1 a 
hundredweight, (a) What is his profit on a ton? (6) 
What is his per cent profit? 

13. A customer ordered 10 T. of coal. The first load 
brought 3500 lb.; the second, 3500 lb. How many pounds 
remained to be delivered? 





.86 


THE BAYNE-SYLVESTER ARITHMETIC 


69. Adding Denominate Numbers 

Elsie visited her grandmother for the holidays. She 
spent 1 hr. 40 min. on the train. Then she had a 25- 
minute ride from the station to the house. How long 
did it take her to make the trip? 


1 hr. 40 min. 

25 min. 

2 hr. 5 min. 


Think: 40 min. + 25 min. = 65 min. 

65 min. = 1 hr. and 5 min. 

Write 5 in minutes' column. 

Add 1 hr. to hours’ column. Write 2. 


1. A milk dealer delivered 2 qt. 1 pt. of milk to his 
first customer, 3 qt. to the second, 1 qt. 1 pt. to the third, 
and 1 pt. to the fourth. How much milk did he deliver 
to all four customers? 

2. How much fence wire is needed to inclose a field 
28 ft. 9 in. on one side, 16 ft. 8 in. on the second, 4 ft. 10 in. 
on the third, and 24 ft. on the fourth side? 

3. Frank and Tom earn money by working after 
school, (a) How many hours did each one work last week? 
(6) At 50^ an hour, how much did each one earn? 


Monday . 
Tuesday . 
Friday . 
Saturday. 

4. 5 gal. 1 qt. 
2 gal. 3 qt. 
4 gal. 2 qt. 


Frank 


Tom 


. 1 hr. 30 min. 

. 1 hr. 20 min. 

. 1 hr. 15 min. 

. 1 hr. 40 min. 


1 hr. 10 min. 
45 min. 

1 hr. 

1 hr. 50 min. 


5. 3 yd. 2 ft. 
1 yd. 1 ft. 
5 yd. 1 ft. 


6. 8 ft. 8 in. 
6 ft. 2 in. 
9 ft. 4 in. 


7. 6 lb. 2 oz. 

5 lb. 8 oz. 

2 lb. 12 oz. 








SEVENTH GRADE 


87 


70. Subtracting Denominate Numbers 

On his first try at the running broad jump, Allan’s 
record was 8 ft. 6 in. On the second try it was 9 ft. 2 in. 
What was the gain in distance? 



6 in. cannot be taken from 2 in. 

9 ft. 2 in. 

Think: 2 in. + 12 in. (1 ft.) = 14 in. 

8 ft. 6 in. 

6 in. + 8 in. = 14 in. 

8 in. 

Write 8 in. 


Think: 9 ft. + 0 = 9 ft. 


In what other way might this subtraction be explained? 

1. The record for the standing broad jump in our school 
was 5 ft. 8 in. Compare the following scores with the 
record. By how much do they fall short of or exceed it? 
(a) 5 ft. 6 in.; (b) 4 ft. 11 in.; (c) 5 ft. 9 in.; (d) 6 ft. 1 in. 

2. A train leaving the city at 2.55 reaches Kingston at 
5.05. How long does it take the train to make the trip? 

3. A crate and its contents weigh 25 lb. 8 oz. The 

crate weighs 12 lb. 12 oz. The contents weigh_ 

4. George is 10 yr. 4 mo. old. His sister is 8 yr. 5 mo. 
old. What is the difference in their ages? 

5. Find the difference between 8 lb. 10 oz. and 16 lb. 
8 oz. 

Subtract: 


6. 12 ft. 5 in. 

7. 9 yd. 1 ft. 

6 ft. 7 in. 

7 yd. 2 ft. 

8. 8 gal. 1 qt. 

9. 5 hr. 15 min. 

5 gal. 3 qt. 

2 hr. 45 min. 








88 


THE BAYNE-SYLVESTER ARITHMETIC 


*71. Multiplying Denominate Numbers 

Mrs. Cook’s milk order is 2 qt. 1 pt. daily. How much 
milk does she receive in a week? 


Think: 7 X 1 pt. = 7 pt. 
7 pt. = 3 qt. 1 pt. 


2 qt. 1 pt. 
7 


Write 1 pt. Carry 3 qt. 
Think: 7 X 2 qt. = 14 qt. 
14 qt. + 3 qt. = 17 qt. 
Write 17 qt. 


17 qt. 1 pt. 


1. Mr. Morris travels 1 hr. 40 min. each day. How 
much does this amount to in 6 days? 

2. What is the total weight of 5 cartons if each weighs 
2 lb. 5 oz.? 

3. WTiat is the distance around a square lot if each side 
measures 24 ft. 10 in.? 

4. How much milk will be delivered to Mrs. Brown in 
2 weeks if her daily order is 1 qt. 1 pt.? 

5. Anna practices 1 hr. 15 min. a day for 6 days a week. 
How much time does she spend at the piano? 

Multiply: 

6. 8 yd. 2 ft. 7. 12 ft. 9 in. 


9 


5 


8. 3 lb. 11 oz. 
4 


9. 1 hr. 10 min. 
7 


10. 5 gal. 2 qt. 
5 


11. 1 sq. yd. 2 sq. ft. 
5 










SEVENTH GRADE 


89 


*72. Dividing Denominate Numbers 

Five packages have a total weight of 12 lb. 3 oz. What 
is their average weight? 



Think: 13 lb. 5 = 2 lb. and a remainder 
of 3 lb. 

2 lb. 10 oz. 

Write 2 lb. over 13 lb. 

5)13 lb. 2oz. 

Think: 3 lb. = 48 oz. 48 oz. + 2 oz.= 

50 oz. 

50 oz. 5 = 10 oz. 

Write 10 oz. over 2 oz. 

The average weight is 2 lb. 10 oz. 


1. Mary spends 7 hr. 30 min. practicing for 6 days a 
week. What is the average time per day? 

2. Agnes had 5 yd. 2 ft. of ribbon, which she cut into 
4 equal lengths. What was the length of each piece? 

3. Stand at a given starting point and then take 6 steps. 
Measure the distance covered. What is the average 
length of your step? 

4. David had three chances at the broad jump. First 
he jumped 4 ft. 11 in., then 5 ft. 3 in., and then 4 ft. 10 in. 
What was his average distance? 

5. A milkman delivers 17 qt. and 1 pt. of milk to Mrs. 
Dodd each week. What is the average daily amount that 
he delivers? 

6. 3)8 gal. 3 qt. 7. 3)19 ft. 6 in. 

8 . 8)17 lb. 8 oz. 9. 7)15 hr. 45 min. 


10. 4)9 yd. 2 ft. 


11. 3)18 hr. 45 min. 










SEVENTH GRADE — PART II 

73. Household Problems 

Without pencil. 

1. Mr. Williams’s salary is $4800 per year. How 
much does he earn per month? 

2. He pays $50 per month for the rent of his apart¬ 
ment. How much does his rent amount to in a year? 

3. (a) What fractional part of his income does he 
spend for rent? (h) What per cent does he spend? 

4. Last winter Mr. Wilhams bought 6 T. of coal at 

$12.50 per ton. The coal cost $_ 

5. In one month the bills for gas and electricity 
amounted to $5.85. The bill for electricity was $2.55. 
What was the amount of the bill for gas? 

6. The bills for electricity for the year amounted to 

$30, the gas bills to $39, and the telephone bills to $33. 
The total amount spent for electricity, gas, and telephone 
was $_ 

7. If Mr. Williams allowed J of his income for food, 
(a) how much money would he spend for food in a year? 
(5) What per cent of his income would be spent for food? 

*8. At the end of the year Mr. Williams found that 
he had spent J as much for clothing as for food. How 
much money did he spend for clothing? 

*9. (a) What fractional part of his income did Mr. 

Williams spend for clothing? (5) This was_% of his 

income. 

*10. (a) How much money did Mr. Williams spend for 

the two items, food and clothing? (5) This was_% 

of his yearly income. 


90 


SEVENTH GRADE 


91 


Use pencil if needed. 

11. A man earns $5040 per year and spends | of it for 
rent, (a) How much does he spend for rent in a year? 
ih) In a month? (c) What per cent of his income does 
he spend for rent? 

12. Mr. Ford earns $450 per month. In January he 
paid of a month’s salary for taxes and $22.50 for 
insurance, (a) How much money did he pay for taxes? 
(6) For taxes and insurance together? (c) What per cent 
of his income was spent for insurance? 

13. On August 5, Mr. Ford paid the following bills: 
gas, $2.75; electricity, $1.95; telephone, $2.25. How 
much money would he have left from a ten-dollar bill? 

14. A man’s income is $4500 per year. He plans to 

spend ^ of it for food and ^ of it for general expenses, 
(a) How much money will he spend for food? (5) For 
general expenses? (c) How much of his salary will be 
left? (d) What fractional part of his salary will be left? 
(c) This is_% of his salary. 

*15. Mr. Ford gives his daughter Mary an allowance of 
$.75 per week and his son John an allowance of $.50 per 
week. In addition, each child receives $5 as a birthday 
gift and $5 to spend at Christmas time, (a) How much 
money does Mary receive per year? (6) How much does 
John receive? (c) Mary receives $_more than John. 

. With pencil. 

16. What is the total cost of the following electrical 
appliances which Mr. Ford bought for use in his home: 
toaster, $7.50; sewing machine, $45; fan, $9.95? 



92 


THE BAYNE-SYLVESTER ARITHMETIC 


17. In October, Mr. Rogers bought 4 T. of coal at 
$12.50 per ton; in December, 3 T. at $12.75 per ton, and 
in January, 3 T. at $13.25 per ton. (a) Find the total 
amount he paid for coal, (b) What was the average cost 
per ton? 

18. What will it cost to install a new hot-water heater 
in the Ford house if the cost of the separate items is as 
follows: heater, $75.90; pipe, 24J ft. at 22^ per foot; 
labor, 8^ hr. at 90^ per hour. 

19. In a district where coal is selling at $12.25 per ton, 
there is an additional charge of 25^ per ton for carrying 
the coal into the cellar. At this rate, what will be the 
total cost of 12 T. of coal? 

20. Mrs. Ford uses If yd. of percale to make an apron. 
How many aprons could she make from 7 yd. of the 
material? 

21. Find the cost of the following purchases made by 
Mrs. Williams: 8^ yd. of percale at 32^ per yard; 3f yd. 
of muslin at 28per yard; and 121 yd. of lace at 16^ 
per yard. 


74. Paying for Electricity 

When the meter man” came into the Shearer home to 
^Yead the meter” on the morning of December 23, Fred 
went to the cellar with him. The meter looked like this: 


1,000 100 10 1 



SEVENTH GRADE 


93 


(It should be noticed that the numbers on the first and 
third dials, reading from the right, go clockwise, but that 
the numbers on the second and fourth dials go in the 
opposite direction.) 

The meter man entered the number 1562 in his book, 
and Fred made a record of the number also. A few days 
later Mrs. Shearer received the following bill: 


To QUEENS COUNTY LIGHTING CO., Dr. 

78 Broadway, Queens, N. Y. 

Nov. 

Dec. 

Meter Readings 

Previous 1 Present 

Used K.W.H. 

Amount 

25 

23 

1504 1562 

58 

$4.06 







Mr. J. B. Shearer, 

192 Main Ave., 
Queens, N. Y. 


Received Payment_ For the Company 


Collector 


On the back of the bill was the following schedule of 
monthly rates for electricity: 

First 1000 K.W.H. — 7 ^ per K.W.H. 

Next 500 K.W.H. — 6 ^ per K.W.H. 

Next 1500 K.W.H. — 5 jzf per K.W.H. 

Next 5000 K.W.H. — per K.W.H. 

Excess — 4 fzf per K.W.H. 













94 


THE BAYNE-SYLVESTER ARITHMETIC 


Fred compared the ‘‘Present Reading’’ on the bill 
with the reading which he made on December 23, and 
found that the readings agreed. The Shearer family had 
used 58 K.W.H. of current, at per kilowatt hour, since 
the previous reading on November 25. The amount of 
the bill was $4.06. Was that correct? 

The amount of electricity used in your home is measured 
by an electric meter furnished by the company which 
supplies you with the current. The unit of measurement 
is the watt hour; 1000 watt hours make a kiloioatt hour. 
The abbreviation for “kilowatt hour” is K.W.H. 


75. How to Read an Electric Meter 



JULY READING 


There are several types of meters, but all are read in the 
same way. The meter has four dials as shown in the 
diagram. Dial 1 (the right-hand dial) registers kilowatt 
hours to 10; the next dial to the left registers kilowatt 
hours by lO’s to 100; the third, by lOO’s to 1000; and the 


SEVENTH GRADE 95 

dial to the extreme left, by lOOO’s to 10,000. Thus the 
meter may be read as a four-place number. 

When the hand in the first dial has made the circuit 
from 0 to 0, the hand on the next dial has moved from 
0 to 1. The same is true of the other dials. When the 
dial hand is between two numbers, read the smaller number. 

The June reading on the meter shown is 6655 K.W.H. 
What is the July reading? How many K.W.H. of current 
were used between readings? Find the cost at 7^ per 
kilowatt hour. 

Notice the ^‘sliding scale” of rates that appeared on the 
back of the Shearer bill. Why did the Shearers have to 
pay the highest rate per kilowatt hour? 


76. Problems 

1. Read the dials below. Compute the amount of 
current used and the cost at 7^ per kilowatt hour. 



MAY READING 


*2. Draw a set of dials to show a reading of 3986 

K.W.H. 


96 THE BAYNE-SYLVESTER ARITHMETIC 

3. The January reading of our meter was 6341, and 
the February reading 6398. At 7per kilowatt hour, 
how much did we spend for electricity for the month? 


4. Yonkers, N.Y. 

Mr. F. J. Spencer 

19-93 Broadway 

To Westchester Lighting Co., Dr. 

Present Reading 4415 

Last Reading 4283 

Used K.W.H. ? 

at per K.W.H. 

Received Payment 

Total $ 

for the Company 

Collector 


5. Bring a bill for electricity from home. Check the 
bill to see whether it is correct. 

6. Read your electric meter today and again a week 
from today. Compute the amount of current used in 
your home for the week. What price do you pay per 
kilowatt hour? 

7. One month ago today, our meter read 5560 K.W.H. 

Now it reads 5985. (a) How much electricity have we 

used? (b) What will it cost at 8^ per kilowatt hour? 

8. The May reading of our meter was 6854. The June 
, reading was 6903. At 8^ per kilowatt hour, what did we 

pay for electricity for May? 







SEVENTH GRADE 


97 


77. Paying for Gas 


100,000 10,000 1,000 



The gas consumed in your home is measured by a meter 
which shows the number of cubic feet of gas used. (Note 
that, as in the case of the electric meter, the numbers on 
the second dial go in the opposite direction from those on 
the other dials.) 

Each division of the right-hand dial represents 100 
cu. ft. of gas. When the hand on this dial has made a 
complete circuit, going from 0 to 0, it means that 1000 cu. 
ft. of gas have been consumed. Meantime the hand on 
the middle dial has moved from 0 to 1. 

Each division on Dial 2 (the middle dial) represents 
1000 cu. ft. A complete circuit of the hand on this dial 
indicates that 10,000 cu. ft. of gas have been registered 
through the meter. 

Can you tell how many cubic feet of gas have passed 
through the meter when the hand on the left-hand dial 
has made a complete circuit? The readings on the meter 
are based on the decimal scale. 

When the hand on any dial is between two numbers, 
read the lesser number. 

Fred read the Shearer meter on June 30 and again on 
July 28, each time just after it had been read by the com¬ 
pany’s reader. 


98 . 


THE BAYNE-SYLVESTER ARITHMETIC 


Here are the meter readings: 



Here is a copy of the gas bill which the Shearers re¬ 
ceived for the month of July: 


To CONSOLIDATED GAS CO., Dr. 


Mr. J. B. Shearer, 
192 Main Ave., 
Queens, N. Y. 


Reading Dates 

Meter Readings 



June 

1 July 

Present | 

Previous 

Gas Used (cu. ft.) 

Due 

30 

28 

39,900 

38,500 

1400 

1.61 


Received Payment_ For the Company 


Collector 












SEVENTH GRADE 


99 


The Shearers pay at the rate of $1.15 per thousand 
cubic feet. Fred checked the bill when it came on July 30. 

July reading 39,900 1400 = 1.4 M. cu. ft. 

June reading 38,500 At $1.15 per thousand, 

Gas consumed 1,400 cu. ft. the cost could be 1.4 X 

$1.15, or $1.61 

The cost of gas. varies from one place to another, but in 
most places it is between $1.10 and $1.40 per thousand 
cubic feet (M cu. ft.). 

A sliding scale’’ of rates is offered by many companies. 
The cost per thousand cubic feet is least to the largest 
consumers of gas. Can you tell why? 

Study your own gas bill with this point in mind. 


78. Problems 


1. Draw a set of dials to show a reading of 17,500 cu. ft. 

2. Find the amount of gas consumed in each case: 


January 1 February 1 


January 1 February 1 


(а) 17,500 22,600 (d) 27,300 29,600 

(б) 87,300 91,400 (e) 72,700 74,500 

(c) 42,100 44,900 (/) 65,900 68,300 


3. In each case above, find the cost of the gas con¬ 
sumed at $1.20 per thousand cubic feet. 

4. Complete the following: 



Present 

Previous 

Amount 

Rate per 

Amount of 


Reading 

Reading 

Consumed 

Thousand 

Bill 

(a) 

47,800 

44,400 

? 

$1.10 

? 

(b) 

44,400 

41,500 

? 

$1.20 

? 

(c) 

62,500 

55,800 

? 

$1.15 

? 

id) 

52,900 

50,600 

? 

$1.20 

? 

ie) 

55,800 

52,900 

? 

$1.05 

? 



100 THE BAYNE-SYLVESTER ARITHMETIC 

5. At SI.20 per thousand cubic feet, find the cost of gas 
consumed in a home in which the meter, as shown by the 
bill, registered as follows: Index, March 1, 34,000 cu. ft., 
index, February 1, 28,000 cu. ft. 

6. If you use gas in your home, read your own meter 
at the beginning of two successive months. Compute the 
amount of gas used. Learn the cost of gas in your locality 
and compute the cost of the gas used in your home for the 
month. 


79. Thrift 

Thrift means more than mere saving. It includes wise 
management of our affairs and careful use of time and 
energy, so that some day we may become efficient workers; 
it includes systematic saving and careful investment and 
wise expenditure of money; it includes looking ahead 
and making provision for the future. 

Benjamin Franklin has sometimes been called the 
“Father of Thrift.” He learned the value of saving and 
wise expenditure of money through his own experiences 
as boy and man. Under the name of “Poor Richard,” 
Franklin wrote many wise sayings, with some of which 
you are more or less familiar. ''A penny saved is a penny 
earned” is one of these sayings. What did he mean by 
this? 

There are several ways of saving money. Some people 
set aside a certain sum each week or each month. The 
money saved should, of course, be wisely invested so that 
it may earn more money. 

To encourage the saving of small amounts, the United 
States maintains Postal Savings Banks in connection with 


SEVENTH GRADE 


101 


its post offices. Here you may deposit ten cents at a 
time. For the ten cents, you receive a stamp affixed to a 
card. Ten stamps may be exchanged for a certificate or 
be redeemed for cash. The certificates bear interest at 
the rate of two per cent per year. The certificates may 
be exchanged for bonds which draw interest at the rate of 
two and one-half per cent per year. Through the Postal 
Savings Banks, many people have been encouraged to 
save small sums of money which otherwise would have 
been spent foolishly. Even a small sum of money, saved 
regularly and invested at compound interest, will soon 
grow into a sum which will surprise you. 

Suppose that you save 5^ each day for 10 years. At 
4% interest, compounded twice a year, your savings of 5^ 
daily will amount to $223.68. 

It is also possible to save by careful buying. The thrifty 
housewife, for example, can save money by being careful 
of her expenditures. Whenever it is possible to do so, 
she will buy staple supplies in quantity, because by so 
doing she saves money. 

Suppose that soap can be bought at 6^ a cake or 65a 
dozen, and that corn can be bought at 18^ a can or 3 cans 
for 50^. How much would be saved by purchasing a 
dozen cakes of soap at a time? Or 6 cans of corn? 

Name three other articles that might be bought in 
quantity. Name three articles that it would be unwise to 
purchase in quantity. 

The thrifty housewife can also save money by paying 
cash for her purchases. Gas and electric companies often 
deduct a certain amount from their bills for prompt cash 
payments. 


102 THE BAYNE-SYLVESTER ARITHMETIC 

Suppose that Mrs. Jones’s gas bill for February is $5.50 
with 5% off for cash within five days. How much does 
Mrs. Jones save if she pays her bill promptly? 

The prompt payment of bills benefits both the buyer 
and the seller. The buyer saves money; the seller bene¬ 
fits because prompt payment helps him to pay his bills 
promptly and saves him the cost of collecting the money 
due him. 

The thrifty housewife can save money by buying at a 
‘‘cash and carry” store. She knows that the grocer who 
maintains an automobile delivery service must charge 
more for his groceries than the grocer whose customers 
carry home their purchases. Why? 

The thrifty housewife can take advantage of sales at 
which articles of food or clothing may be purchased at 
reduced rates. 

80. Problems 

1. At a sale of gloves the following reductions were 
made: 

$1.15 quality for 85ff $1.75 quality for $1.35 

$1.50 quality for $1.00 $1.95 quality for $1.65 

$1.65 quality for $1.20 $2.25 quality for $2.00 

How much would be saved by buying (a) two pairs of 
the $1.95 quality at the sale? (b) A pair of the $1.65 
quality? 

2. At a clearance sale of furniture, the following prices 
were quoted: 

Davenport table formerly $75.00 now $39.50 

Arm chair formerly $175.00 now $137.50 

Hall chair formerly $185.50 now $145.75 

Rocker, mahogany formerly $87.50 now $65.00 


SEVENTH GRADE 


103 


(a) At the sale, the davenport table is sold for $ _ 

less than its former price; (b) a hall chair is sold for $ _ 

less than its former price; (c) Mrs. Hall bought an arm 

chair at the sale. She saved I _ (d) Find the total 

saving on the four articles if purchased at the sale. 

3. The following is the price list advertised by a 
grocery store for a week-end sale: 


Article 

Regular Price 

For This Sale 

Apricots .... 

21 i can 

2 for 49 

Pears. 

35^ can 

2 for 68^ 

Peaches .... 

32 can 

2 for 58|zf 

Soap, naphtha 

6^ cake 

6 for 30^ 

Soap, Ivory . 

bji cake 

6 for 25^ 

Rice flakes 

15^ box 

2 for 25^ 


Imagine yourself to be the. grocery clerk. 

Customer A buys 4 cans of apricots, 2 cans of pears, 
and 2 boxes of rice flakes, (a) What does she pay for 
these articles at sale prices? (h) How much does she 
save? (c) How much change should she receive if she 
pays for her purchases with a flve-dollar bill? 

4. Customer B buys 6 cakes of naphtha soap, 4 cans 

of pears, and 2 cans of apricots, (a) She spends $_ 

(b) Buying at sale prices, she saves $- 

5. How much would a customer save by buying 6 
cans of pears at the sale instead of buying 1 can at six 
different times? 

*6. By paying his bill within 10 days, Mr. Frank was 
allowed a 2% reduction on his coal bill. He bought 6 T. 
of coal at S12.75 per ton. (a) How much money did he save? 
(b) What would he save on 8 T. at $14.75 per ton? 




104 THE BAYNE-SYLVESTER ARITHMETIC 


7. For each of the following, find the amount of 
money saved by paying cash: 

Amount 


Article 

Cost Off for Cash 

Saved 

Gas range 

. $75.00 

10% 

? 

Table (kitchen) 

$12.50 

5% 

? 

Davenport . 

. $187.50 

15% 

? 

Buffet 

. $95.00 

12M% 

? 

Dining table 

. $47.50 

10% 

? 

8. A dealer offered 12% off for cash 

on a table costing 


$75.50. How much would a customer save by paying 
cash? 


9. A grocer received a bill of $750.75 with 5% off if 
paid within 10 days. Find the amount he saved by 
prompt payment of the bill. 

10. The Browns’ gas bills for the first six months of 
last year were as follows: 


January $4.50 March $4.25 May $4.35 

February $4.75 April $4.00 June $3.80 


If Mrs. Brown is allowed 2% off on each bill for prompt 
payment, how much does she save (a) in each month? 
(5) In the six months? 

11. For payment at the time of purchase, a wholesale 
dry-goods merchant allows a reduction of 5% from the 
amount of the bill. How much will Mr. Johnson save 
on a bill of $550.80 by cash payment? 

12. Bring in a bill from your home, showing a reduc¬ 
tion for prompt payment; or a reduction for a quantity 
purchase; or a reduction granted at a sale. 


SEVENTH GRADE 


105 


81. Order Blanks 

Mr. James is preparing to plant a garden this spring. 
He has selected his seeds from the catalogue of Jones, 
Robinson, and Brown, Seedsmen, of Boston, Massa¬ 
chusetts. The following is his order, prepared on the 
order blank found in the catalogue: 


JONES, ROBINSON, AND BRO 
Seedsmen 

64 Commercial Street 
Boston, Massachusetts 

Name: John B. James, Jr. 

Residence or P. 0. Address: Chestnut Ave. 

Citv: Germantown State: R.F.D. 

How sent? Parcel Post Amount inclosed 

WN 

$ 2 . 4.0 

)rder 

Catalogue 

Number 

Quantity 

Name of Article 





B 3759 

B 3942 

L 374 

L 379 

3 pkt. 

3 pkt. 

2 pkt. 

3 pkt. 

Stringless Bean 

Bush Lima Bean 

Cos Lettuce 

Brittle Ice Lettuce 

Total amount 


25 

30 

15 

15 


75 

90 

30 

45 


2 

40 


How many items are ordered? What is the total 
amount of the order? How are the seeds to be sent? 
How did Mr. Jones pay for the seeds? 

Many large business concerns issue order blanks in 
connection with their catalogues. Ordering goods by 
means of these blanks saves time for both the dealer and 

















106 THE BAYNE-SYLVESTER ARITHMETIC 

the customer. It is easy, too, for the dealer to keep these 
uniform order blanks on file for reference. 

Mr. White wishes to send The Sportsman’s Magazine 
to his friend Mr. Dick as a Christmas gift. This is the 
order blank which he will use: 


THE SPORTSMAN’S MAGAZINE 
285 Main St., Garden City, L. L, N. Y. 

Enclosed is check for $2.50, for which kindly enter a gift 
subscription to 

The Sportsman’s Magazine 

to be sent to the following address until January, 1931: 
Send to: Mr. J. B. Dick Sent by: Fred J. White 

Address: 3284 South St. Address: 87 Juniper St. 

City: Brooklyn City: Hyde Park 

State: N. Y. State: III. 


Who will receive the magazine during 1930? Who 
sends it? How is payment made for the subscription? 

Write an order form for a year’s subscription to St. 
Nicholas Magazine to be sent by you to your cousin. 
Supply all the necessary information. 

82. Sales Slips 

When you make a purchase at a department store, the 
clerk who serves you makes out two copies of a sales slip. 
One copy is inclosed in the package with your purchase; 
the other copy is retained by the clerk. This sales slip is a 
record of your purchase. The following is a common 
type of sales slip: 



SEVENTH GRADE 


107 


FRANK E. DAVIS CO. 



Dry Goods 

384 Fourth Ave. 
Newton, N. Y. 



Feb. S, 1930 

Name: i^i^s J. E. Fort 

Address: 74^ Sinclair Rd. 

Amt. Rec’d. $20.00 

12 yd. Lace @ .30 

3 

60 

1 pr. Silk Hose @ 1.95 

1 

95 

1 doz. Napkins @ 7.50 

3 

75 

1 Table Cloth @ 6.00 

6 

00 


15 

30 


Where were the goods purchased? To whom were they 
sold? How many items were purchased? 

The total amount paid for each item is called the exten¬ 
sion. Adding all the extensions to find the total is called 
footing the bill. 

What is the total amount of the purchase? How much 
money did Miss Fort give the clerk in payment? 

Sales slips are always made out at the time that a pur¬ 
chase is made. The sale may be a cash sale or a sale on 
account. Look at the sales slips which you receive when 
you make purchases at different stores. What differences 
do you notice? 














108 


THE BAYNE-SYLVESTER ARITHMETIC 


J. J. Dodd 

BUTTERCUP DAIRY 

Dealer In 

Butter, Cheese, and Eggs 

305 Elm St. 

TpI M>,m 4.'Sfi N. Y., Dec. 1, m9 

Sold t 

r, Mrs. Frank Dean 

ISk East 182 St. 


Dec. 

1 

2 lb. Sweet Butter @ .62 

1 

24 



i lb. Salt Butter @ .56 


28 



1 doz. Eggs @ .70 


70 




2 

22 



Received Payment 





Dec. 1, 1929 





J. J. Dodd 





per L. L. A. 




Here is a sales slip from a dealer in dairy products. 

The purchaser has paid for the goods. You will note 
that the slip has been receipted. On what date was pay¬ 
ment made? Did the owner of the store receipt the slip? 

1. Imagine yourself to be a clerk in a large grocery 
store. Make out sales slips for the following purchases. 
Supply all the necessary information: 
































SEVENTH GRADE 


(a) 3 cans Peas @ 18^ 

2 lb. Butter @ 55^ 

^ doz. Eggs @ 68^ 

(c) f lb. Cheese @ 40^ 

3 lb. Potatoes for 14^^ 
3 cans Corn for 50^ 


109 

(6) 2 loaves Bread @12^ 
3i lb. Sugar for 27^ 

2 lb. Coffee @ 48^ 

(d) ^ lb. Tea @ 90^ 

3 cans Milk @9^ 

1 can Cocoa @ 22^ 


2. Bring to class an advertisement from a daily paper. 
Make up two sales slips, using the prices given in your 
advertisement. Supply all other necessary information. 


83. Bills 

When a customer does not pay cash at the time of pur¬ 
chase, a hill or statement is sent to him at the end of the 
month. 

A bill is a written statement of the amount of money 
due a creditor for materials purchased or for service 
rendered. A bill often contains the terms on which a 
sale is made. 

Though they may differ in certain details, both sales 
slips and bills contain the following items: 

1. The name and address of the merchant or dealer 
who makes the sale. 

2. The name and address of the purchaser. 

3. The date on which the purchase was made. 

4. The cost of each item purchased. 

5. The total amount of the purchase. 

A sales slip is a record of purchases made on one day ; 
a bill is frequently a record of sales made on different 
days. 


no 


THE BAYNE-SYLVESTER ARITHMETIC 


Mr. Farley is having his house painted. He purchased 
his supplies from Smith and Jones, dealers in hardware 
and paints, on September 20 and 22. On October 1 he 
received the following bill: 


Terms: Monthly Settlement 


SMITH AND JONES 
Hardware and Paints 
1482 Broadway 
Brooklyn, N. Y. 

Oct. 1, 1929 

D. J. Farley 
30 South Street 
Brooklyn, N. Y. 


Date 

Description 



Sept. 

20 

10 gal. Sun Paint @ 4.50 

45 

00 





3 gal. Dryer @ 2.75 

8 

25 




22 

5 gal. Sun Paint @> 4.50 

22 

50 

75 

75 



Received Payment 

October 10, 1929 

Smith and J ones 







Per L. A. H. 






Are the extensions correctly made? Is the footing cor¬ 
rect? 

When was the bill paid? 

Did Mr. Smith or Mr. Jones receipt the bill? 

Make out a bill showing purchases made on three 
different days. Receipt the bill. 











SEVENTH GRADE 


111 


Bills for materials and labor differ slightly from the bills 
you have just studied. 

The mechanic or contractor who makes repairs on your 
house not only charges for materials used, but he also adds 
a charge for his labor. 


Monmouth, N. J. 
May 1, 1930 


Mr. J. B. Sprague 
238 John Street 
To Robert Davison, Dr. 


Apr. 

5 

3 qt. White Clover Seed @1.25 

3 

75 




8 hr. Labor on Lawn @ .50 per hour 

4 

00 


Apr. 

6 

4^ hr. Labor on Lawn @ .50 per hour 

2 

25 

10 



Received Payment 





May 7, 1930 






Robert Davison 





(Dr. means debtor, one who owes. Cr. means creditor, 
one to whom money is owed.) 

1. Mr. F. A. Osgood, a plumber in Huntington, L. I., 
did repair work for Mr. W. B. Collins of the same town. 
The plumber supplied 19 ft. of copper leader at 40^ per 
foot, and charged $1.25 per hour for labor. He worked 
2 hr. 30 min. Make out the bill. 

2. Perhaps your house has been wired for electricity 
or your father has had the kitchen painted, or your 
mother has had new covers made for the living-room 
chairs. Make out a bill for any one of these items. 

Be careful to learn the current prices for labor and 
materials. 











112 THE BAYNE-SYLVESTER ARITHMETIC 

Doctors, dentists, lawyers, and other professional men 
send bills in somewhat different form, as you will notice 
from the one below: 


HENRY J. MOORE, M.D. 

40 E. 41 St., N. Y. 

Dec. 1, 1929 

To Miss E. K. Leonard 
21 W. 49 St., N. Y. 

For professional services $25.00 


Received Payment 
Dec. 19, 1929 
Henry J. Moore, M.D. 
Per M. E. Parker 


Dr. A. A. West, a dentist having an office at 75 W. 
181 St., N. Y., presents his bill for $72.50 to Mr. James L. 
Lee, of Westbury, L. I., for professional services on July 
12 and 16. Make out the bill. 


84. Getting a Receipt 

When a purchaser pays a bill, he should be given some 
proof that the bill has been paid. Such proof usually 
takes the form of a receipt. 

On some of the bills you have just studied, you have 
noticed one form of receipt. 

Sometimes another type of receipt is used. Two forms 
are shown here. How do they differ? 



SEVENTH GRADE 


113 


Received from John Moore 

New York, 24, 1929 

in settlement of his account 

hni'y> rtv/jri ri'yirl 0 0 — — — — —_ 

— — — — — — — — — - — — — — ^ 


$200^\ 

Samuel Brown 



Received from James Walker 

Dec. 16, 1929 

On account 


________ _ _ / 1 /~k///^/v*r» 

kJTI/G flUYlCLV&Ct CLTl/Ct i o 0^ ^ ^ 

xyot/t/U'/ o 

$100^^ 

Allan Stuart 



A receipt may be in full settlement of an account or it 
may be for only part of the amount due. 

Why is the amount written twice? Why should all 
receipts be kept? 

Write a receipt for each of the following, supplying 
needed facts that may have been omitted: 

1 . John Allen borrowed $500 from Henry Wise. On 
June 6, he paid the amount in full. 

2. On August 1, Joseph Dane received $750 from 
James Burden in part payment of his account. 

3. J. M. Noble received $55.24 from John Alexander 
in payment of a bill. The money was paid May 25. 




















114 


THE BAYNE-SYLVESTER ARITHMETIC 


4. Imagine that you are the treasurer of a club. Write 
a receipt for dues received from a member of the club. 

5. Write the receipt Dr. Simms gave Anna Perkins 
when she paid him $75 in full settlement of her account. 

6. Dr. Brandon received $50 on account from Mrs. 
Baird. Write the receipt he gave her. 

7. Write a receipt for rent of the premises at 84 
Bradford Ave. for March 19. The tenant is Mr. K. L. 
Ford; the owner, Mr. F. E. Lyman; the rent, $75.50 
per month. 

8. Bring in a receipt from home. Explain it to your 
classmates and teacher. 

9. Fred Smith bought a basket ball from you for $5. 
Write a receipt for him. 

10. Your mother pays a grocery bill of $7.50 to Mr. 
F. J. Brown, of 484 Main St. Write the receipt. 

11. Mr. F. F. Jennings owes Mr. J. F. Stanley $500. 
He pays Mr. Stanley $250 on account. Write the 
receipt. 

12. Suppose that Dr. J. F. Linton made five visits to 
your home while you were ill and that he charged $5 a 
visit. Make out the bill he would send to your father for 
his services. 

13. Read again the “Smith and Jones'’ bill on page 
110. Write a similar bill for the following supplies pur¬ 
chased by Mr. Farley: 

3 Sun Brushes @ $.85 1 can Floor Varnish @ $1.85 

2 gal. Floor Paint @ $4.85 2 cans Floor Stain @ $.95 

Supply all necessary information. Receipt the bill, 
using your own name. 


SEVENTH GRADE 


115 


Sometimes bills are paid by check. A check is a written 
order on a bank to pay a certain amount of money to the 
person whose name appears on the/ace of the check. The 
signer of the check must have enough money on deposit 
in the bank to cover the amount called for by the check. 
A form of check is shown below: 


No _New York_ 19_ 

CENTRAL TRUST COMPANY 
Pay to the 

ORDER OF_$_ 

__Dollars 


The returned check acts as a receipt. Therefore, it is 
wise to keep all checks returned to you by the bank. 

85. Profit and Loss 

Mr. Henry sells furniture. He bought tables at S35 
each and sold them at S45.50 each. What was the differ¬ 
ence between the cost and the selling price? 

When an article is sold for more than its cost, it is said 
to be sold at a profit. What was the amount of profit on 
each table sold by Mr. Henry? 

When a man invests his money in any line of business, 
his object is, of course, to make a profit on his investment. 
To do this, he must sell his wares for more than they cost 
him. 










116 


THE BAYNE-SYLVESTER ARITHMETIC 


The cost of an article, however, usually includes more 
than just the sum of money paid for it. For example, 
the cost of Mr. Henry’s tables — $35 each — is but one 
item in Mr. Henry’s expense account as a furniture dealer. 
In addition to buying his stock, he must pay rent; he 
must pay for light, heat, and telephone service; he must 
pay salaries to his employees; he must carry insurance to 
protect his stock. 

The expenses necessary to carrying on the business are 
called overhead expenses or simply overhead. If you think 
for a moment, you will readily understand that overhead 
expenses may run into quite a large sum. 

A study of the retail trade in several lines has just been 
completed. It shows that, in the United States, the 
overhead in clothing, hardware, shoes, dry goods, and 
other lines may range between 20% and 30% of the first 
cost. 

Mr. Henry may find that he cannot sell his tables readily 
at $45.50 each; he may therefore be forced to reduce them 
below cost, and so suffer a loss. 

In fixing upon the selling price of an article, a merchant 
must consider (1) first cost, and (2) overhead. The cost of 
an article plus the overhead equals the total cost. In order 
to yield a profit on the investment, the selling price must 
be sufficient to cover (1) first cost, plus (2) overhead, plus 
(3) profit on the investment. 

In these exercises, unless it is otherwise stated, profit 
and loss (and the per cent of profit or loss) will be reck¬ 
oned on the total cost.^ 

1 Profit and loss and the per cent of profit and loss are sometimes based 
on cost and sometimes on selling price. 



SEVENTH GRADE 


117 


1 . Tell at sight the amount of profit: 




Selling 




Selling 



Cost 

Price 

Profit 


Cost 

Price 

Profit 

(a) 

$.16 

$.20 

? 

ie) 

$7.50 

$10.00 

? 

(b) 

$16.00 

$25.00 

? 

if) $50.00 

$62.50 

? 

(c) 

$20.00 

$22.50 

? 

ig) 

$3.80 

$4.60 

? 

id) 

$.50 

$.85 

? 

ih) 

$9.60 

$12.00 

? 

2. 

An article sold 

for $60. 

Its 

cost 

was $45. 

The 


gain was 


3. Mr. Henry paid $42.75 apiece for desks which sold 

at $50 each. The profit on each desk was_ 

4. Mr. Jones deals in radios. On a certain radio, the 
first cost is $74.50 and the overhead $5.50. If the radios 
sell at $90 each, what is the profit on each? 

5. Tell at sight the amount of loss: 


Selling Price 

Cost 

Loss 

Selling Price 

Cost 

Loss 

ia) $10.50 

$12.00 

? 

id) $.54 

$.75 

? 

(6) $7.85 

$10.00 

? 

(e) $6.50 

$7.75 

? 

(c) $.95 

$1.10 

? 

if) $3.20 

$4.00 

? 


6. Mr. Ames paid $700 for a car, and was forced to sell 

it for $635. He lost_ 

7. Suits that cost $48.50 were sold at an end-of-the- 

season sale for $42. This meant a_of_on each 

suit. 

8. Mr. Putnam manufactures washing machines. 
The first cost of each machine is $90 and the overhead 
is $30. If Mr. Putnam sells each machine for $150, 
(a) what is the amount of his profit? (6) What is the 
per cent of profit? 



118 


THE BAYNE-SYLVESTER ARITHMETIC 


86. Finding Profit or Loss 

A suit that cost $45 was sold at a 20% profit. Find 
the profit. 


1 $9 

20% = .20 = T% = i $9 profit 


To find the profit or loss, multiply the cost by the 
per cent of profit or loss. 


This is the same as finding a_of a number. 

Without pencil. 

1. An article that cost $3.60 was sold at a profit of 25%. 
What was the profit? 

2. Coats which cost $60 each were sold at a gain of 30%. 
Find the gain. 

3. Find the profit on an automobile bought for $800 
and sold at 25% profit. 

4. A phonograph which cost $48 was sold at 16|% 
profit. What was the profit? 

5. A coat that cost $40 was sold at a loss of 20%. 
Find the loss. 

6. A man paid $700 for a used car and sold it at a 10% 

loss. He lost_ 

7. A dealer paid $740 for a piano and was forced to 

sell it at a loss of 30%. His loss was_ 






SEVENTH GRADE 


119 


87. Finding the Selling Price 

A suit that cost $45 was sold at a profit of 20%. 
(a) Find the profit, (b) Find the selling price. 


1 ' $9 

g X $9 = profit $45 + 9 = $54 = selling price 


Selling price equals cost plus profit or cost minus 
loss. 


1. A farm which cost $12,000 was sold at a gain of 
25%. For what price was it sold? 

2. Mr. Henry sells davenports for which he paid $156 
each at a gain of 331%. What is the selling price? 

3. A watch which cost $120 was sold at a loss of 12 J%. 
For what price was it sold? 

4. A consignment of cotton cost $1800. It was sold 

at a loss of 16f%. The selling price was- 

5. What price must a dealer ask for a piano that cost 
$950 in order to make a profit of 30%? 

6. Mr. James has purchased a machine for $750. He 
wishes to make a profit of 35% on his purchase. For 
what sum must he sell it? 

7. Mr. Henry paid $42 for a chair. For what must 
he sell it to make a profit of 16f%? 

8. I bought a farm for $9500. I spent a sum equal to 
20% of the purchase price on improvements. What must 
I sell it for to gain 20% on my investment? 





120 


THE BAYNE-SYLVESTER ARITHMETIC 


9. Complete: 

(а) The total cost of an article includes the-and 

the_ 

(б) When an article is sold above cost, it is sold at 

a_ 

(c) When sold at a loss, an article is sold-cost. 

(d) In addition to the actual cost of an article, there 

are usually other items of expense, such as-and- 

These are called_ 

10. Mr. Miller bought an automobile for $300. He 
spent $180 on it for repairs and painting. What must he 
sell it for to gain 40%? 

88. Finding the Per Cent of Profit or Loss 

Without pencil. 

A coat which cost $45 was sold at a gain of $15. Find 
the per cent of gain. 


$15 is what per cent of $45? H i = . 33 | = 33 |% gain 
Check: 33 ^% = i i X $45 = $15 


Finding the per cent of gain is like finding what per cent 
one number is of another. 

1. Tell at sight the per cent of gain or loss: 



Cost 

Gain 


Cost 

Loss 

(a) 

$250 

S50 

(/) 

$200 

$50 

(b) 

$8 

fl 

ig) 

$12 

$2 

ic) 

$15 

13 

Qi) 

124 

$3 

(d) 

$2400 

S600 

ii) 

$1600 

$200 

(«) 

$25 

$5 

(i) 

$75 

$25 





SEVENTH GRADE 


121 


2. A book which cost $2 was sold at a gain of $.50. 

The rate of gain was_ 

3. A radio which cost $100 when new was sold six 
months later at a loss of $25. What was the per cent 
of loss? 

4. Articles which cost $10 each were sold at a loss 

of $2 because of damage by fire. The per cent of loss 
was_ 

5. A pen which cost a dealer $10 was sold for $14. 
(a) What was the gain? (b) What was the gain per cent? 

6. Mr. Ford bought dress goods at $4.50 per yard and 
sold it for $6 per yard. What was the per cent of profit? 

With 'pencil. 

7. A horse bought for $125 was sold for $105. The 

per cent of loss was_ 

8. An automobile costing $1250 is sold for $1050. 

The rate of loss is- 

9. A building cost $11,000. The owner spent $1680 
on repairs. He then sold it for $14,000. What per cent 
did he gain on the total cost? 

10. A merchant bought 240 yd. of silk at $l| per yard. 
He sold it at a gain of $54. What per cent did he gain? 

11 . At a special sale, furniture was marked down as 
follows: 

Original Price Sale Price 

Tables 172 $60 

• Chairs $27 $21 

On which of the two articles was the per cent of reduc¬ 
tion larger? 




122 THE BAYNE-SYLVESTER ARITHMETIC 

12. A desk chair cost Mr. Henry $12.50. What per 
cent would he gain by selling it for $15? 

13. Fur coats were priced $240 in November. At a 
January sale they were sold for $192. What per cent 
reduction was made? 

14. If the cost of an article is $5.60 and the selling 
price is $7.28, what is the gain per cent? 

89. General Review of Profit and Loss 

Without pencil. 

1. A coat costing $24 was sold at a gain of 25%. The 

selling price was_ 

2. Eggs bought at $.48 per dozen are sold at a gain of 

12|%. The selling price per dozen is_ 

3. At the end of the season Miss Price, a milliner, sold 
a hat which cost $12 at a loss of 16f%. How much did 
she receive for the hat? 

4. At what price must I sell a book which cost $1 to 
make a profit of 20% ? 

5. Fish bought at 12^ per pound is sold so as to gain 

33j%. It sells for_per pound. 

6. Sam paid $5 for a dog. At what price must he 
sell it to gain 25%? 

7. Mr. Jones bought a lot for $2400. He was forced 
to sell it at a loss of 25%. How much did he get for it? 

8. Mr. Williams bought a lot for $1300. He spent 
$200 for taxes and improvements. For what price must^ 
he sell it to gain 20% on his investment? 

9. A horse was bought for $125 and sold at a loss of 

8%. It was sold for_ 






SEVENTH GRADE 123 

*10. I bought a house for $8000. How much rent must 
I charge per month to make 9% on my investment? 

Use pencil if needed. 


11. Complete: 


Cost 

Selling Price Gain Loss Rate of Gain or Loss 

(a) $6400 

$6784 

(6) $12,000 

$12,700 

(c) $1500 

$1000 

(d) $48,000 

$42,000 

(e) $24,000 

$27,000 

(J) $8500 

$9010 

(g) $12,600 

$11,400 

(h) $16,000 

$16,400 

12. James bought a pair of skates for $3.75 and sold 
them at a profit of $.50. What was the per cent of profit? 

13. What 

is gained by the sale of 8 lots, costing $1500 

each, if they 

are sold at 35% profit? 

14. Find the profit on 150 T. of coal bought at $8.50 
per ton and sold at a gain of 20%. 

15. Shoes cost a dealer $4.80 a pair. He sells them at 
an advance of 14%. How much will he gain on 175 pairs? 

16. Complete: 

Cost 

Gain % Gain Loss % Loss Selling Price 

(a) $7.50 

10 

(6) $95.00 

15 

(c) $42.50 

10 

(d) $180.00 

35 

(e) $37.50 

20 

(/) $56.00 

12 


THE BAYNE-SYLVESTER ARITHMETIC 


124 



Cost 

ig) 

$5.75 

ih) 

$16.64 

(t) 

$7.75 

(i) 

$372.00 

(k) 

$17.28 


Gain% Gain 

40 


Loss% Loss 

40 

75 

16f 


Selling Price 


This was 20% 


90. Finding the Cost 

A dealer sold a house at a gain of $1200. 
of its cost. What did the house cost him? 


$1200 = 20% of what number? 

20% = i 

$1200 = ^ of the cost 
f of the cost = 5 X $1200 = $6000 = cost 
. $1200 

Check: ^ of J£mr= $1200 


This problem is like a problem in finding a number 
when a per cent is given. 

1. A dealer sold a popular biography at a gain of 25%. 
His profit on each copy was $1.84. What did each copy 
cost him? 

2. Father sold potatoes at a profit of $217.50. What 
did they cost him if the rate of profit was 15%? 

3. When the gain on an article is $3.60 and the rate of 
gain is 20%, what is the cost? 

4. A consignment of cotton was sold at a profit of 
16f%. The amount of profit was $325. What was the 
cost of the cotton? 



SEVENTH GRADE 


125 


91. Commission 


The Talbot Farm in our town was divided into building 
lots. A real-estate agent sold a lot to Mr. Preston for 
$1200. He received as his fee 5% of the amount for 
which the lot was sold. How much money did he receive? 


$60 


1 


5% = 


_A_ = _JL 

1 0 0 2 0 



The agent received $60. This was his pay or commission 
for selling the lot. 

Commission is one of the business applications of 
percentage. Many persons earn their living by selling 
goods or property for others. For this service a certain 
sum is charged. This charge is called commission. Thus, 
when a real-estate agent buys and sells real estate or 
collects rents, his pay for his services is called commission. 
Similarly, in addition to his salary, a salesman is often 
allowed commission on the amount of goods he sells. 
Brokers, also, receive a commission for buying and selling 
stocks and bonds for their customers. 

A commission merchant buys and sells produce. For 
doing this he charges a certain per cent of the amount of 
the transaction. This charge is called his_ 

The commission is the amount a person receives for 
selling goods or property, or transacting business for 
another. Commission is often expressed as a certain 
per cent. This per cent is called the rate of commission. 




126 


THE BAYNE-SYLVESTER ARITHMETIC 


An agent, working on a 5% commission, makes a sale 
amounting to $575. How much does he receive as his 
commission? 


A. 5% = .05 

B. 5% — xf 0 — w 

$575 

1 $115 

.05 

.1575^= ^ = S28i or $28.75 

$28.75 commission 

4 


commission = $28.75 


To find the commission, change the rate of com¬ 
mission to its decimal or fractional equivalent. Then 
multiply the value of the goods bought or sold by this 
decimal or fraction. 


This is the same as finding a per cent of a number. 


Use pencil if needed. 

1. Find the amount of commission on each of the 
following sales at the rates given: 


Amount of 

Rate of 

Amount of 

Rate of 

Sale 

Commission 

Sale 

Commission 

(a) $900 

5% 

(e) $9750 

8% 

(6) $1700 

3% 

(/) $150.50 

4% 

(c) $1890 

2% 

(g) $1785.25 

5% 

(d) $1200 

6% 

(h) $75.75 

3% 

2. What is the commission, at 3%, on $200 worth of 

goods? 

3. An agent 

sells $540 worth of goods at 2% com- 

mission. He receives- 

for this service. 









SEVENTH GRADE 127 

4. At 5% commission, how much would an agent 
receive for selling a lot for $1500? 

5. A lawyer collected a debt of $1950, charging 10%. 

His commission amounted to _ 

*6. A commission merchant charging 10% sold 100 bbl. 
of potatoes at $4.50 a barrel. How much money did he 
receive? 

*7. An agent sold a piece of property for $3600. The 
rate of commission was 2^%. What was the amount he 
received? 

*8. Our town has contracted to build a new junior 
high school that will cost $450,000. The architect who 
drew the plans received a commission of 6%. WRat was 
the amount of his commission? 

92. Finding the Net Proceeds of a Sale 

Mr. Preston paid the agent $1200 for one of the Talbot 
Farm lots. The agent’s rate of commission was 5%. 
Therefore, he kept $60 (5% of $1200) and sent, or re¬ 
mitted, to Mr. Talbot $1140. This amount is called the 
net proceeds of the sale. ' It is the amount left after the 
commission has been deducted. 

An agent, working on a 5% commission, collected a 
debt amounting to $575. (a) What was his commission? 

(6) How much did his employer receive? 


$575 amount collected 

$575.00 amount collected 

.05 rate of commission 

$28.75 commission 

$28.75 commission 

$546.25 net proceeds 






128 


THE BAYNE-SYLVESTER ARITHMETIC 


To find the net proceeds, subtract the commission 
from the selling price. 


With pencil. 

1. A real-estate agent collects $5750 in rents each 
month. He charges 3% commission, (a) How much 
does he receive each month? (5) How much does he 
remit to the owner? (c) What will his commissions 
amount to in a year? 

2. A commission merchant sells 1500 bu. of wheat, at 
$1.25 per bushel, charging 5% commission, (a) How 
much does he receive for this service? (6) What are the 
net proceeds of the sale? 

3. A real-estate dealer sold a piece of property for 

$15,000. The rate of commission was 3|%. (a) How 

much did the owner receive? (5) What was the agent’s 
commission? 

4. Mr. Pratt’s salary as a salesman is $40 per week. 
In addition, he receives a commission of 2% on sales. 
His sales last week amounted to $750. Find his total 
income for the week. 

5. A lawyer collected 85% of a debt of $1500. The 

rate of commission was 5%. (a) How much money did 

the lawyer collect? (6) What did his commission amount 
to? (c) How much should he remit to the creditor? 

*6. A fruit grower shipped 1200 baskets of peaches to 
a commission merchant, who sold them at $.75 per basket. 
Freight charges amounted to $45.50; the rate of com¬ 
mission was 3%. (a) What was the agent’s commission? 

(5) How much money did the grower receive? 



SEVENTH GRADE 


129 


7. A commission merchant sold 120 bbl. of apples at 
S6.75 per barrel, and charged a 2|% commission. How 
much did he remit to the owner? 

8. A real-estate dealer sold 6 lots at $1500 each, and 

received 5% commission. His commission amounted to 
$_The owner received $_ 

9. Find the commission and the net proceeds on the 
following sales: 


(a) 1600 at 3% 

(b) $1200 at 3^% 

(c) $980 at li% 

(d) $1275 at 6% 


(e) $175.28 at 4% 

(/) $475.85 at 12^% 

(g) ' $1680.50 at 5% 

(h) $850.00 at 20% 


93. A Short Way of Finding the Net Cost 

At a sale, a coat regularly listed at $175.50 was sold at a 
discount of 20%. Find the net cost. 

The list price of the coat equals 100% of itself. If the 
coat is sold at a discount of 20%, it is sold for 80% of the 
list price. (100% — 20% = 80%.) Therefore, the net 
cost is 80% of $175.50. 


A. 

B. 

80% = .80 

80% = .80 = = |- 

.80 of $175.50 = $140.40 = 

4 $35.10 

net cost 

1 of |175:5fr= $140.40 = 

^ net cost 


1. A sewing machine listed at $85.75 was sold at a 
discount of 15%. For what price was it sold? 

2. When an article is sold at 25% discount, the net cost 

is_% of the list price. 







130 THE BAYNE-SYLVESTER ARITHMETIC 

3. What per cent of the list price is paid for goods 

bought (a) at a discount of 331%? (b) At a discount of 

16f%? 

4. Find the net cost of 42 pairs of gloves at $2.50 a 
pair, less 30%. 

5. At a sale Carl bought a pair of hockey skates listed 
at $11.50 at ^ off. How much did the skates cost Carl? 

6. In each of the following examples, find the net cost 
in two ways: 

List Price Discount List Price Discount List Price Discount 

(a) $45 i off (e) $58.50 10% (i) $7.50 J off 

(5) $85 20% (/) $74.80 25% (i) $1624.50 40% 

(c) $300 12i% {g) $59.40 33|% {k) $1800 15% 

(d) $568 37i% Qi) $120.20 6% ® $880 71% 

94. Review of Terms in Commission 

1. A person who buys, or sells, or transacts business for 

another is called an-or a- 

2. The sum charged by an agent for transacting the 

business of another is called the- 

3. The commission is a certain per cent of the amount 

of money involved in the business transaction. This per 
cent is called the_of commission. 

4. Agents often buy as well as sell for others. When a 

purchase is made, the agent reckons his commission on 
the amount of money involved in the purchase. When a 
sale is made, the commission is reckoned on the amount 
of_ 

5. The commission is deducted from the amount of 

money involved in the sale. The difference is remitted to 
the_This difference is called the- 










SEVENTH GRADE 


131 


95. Interest 

Mr. Elliott decided to increase his stock of merchandise 
in preparation for the spring trade. To do this, he bor¬ 
rowed $2000 from the Gotham Bank for a year. At the 
expiration of that time, the bank charged Mr. Elliott 
6% of $2000, or $120, as payment for the use of the $2000. 
This extra sum, $120, is called interest. 

The $2000 which Mr. Elliott borrowed is called the 
principal. Interest is always computed as a certain per 
cent of the principal. This per cent is called the rate, or 
the rate of interest. In this case, it was_%. 

The period for which the principal is borrowed is called 
the time. The time in this case was one year. If Mr. 
Elliott borrowed the $2000 for two years, he would pay 
twice as much interest, or $_ 

Interest is money paid for the use of money. 

When Mr. Elliott settled his account with the bank at 
the end of the year, he paid $2000 (principal) and $120 
(interest), or $2120. The sum of the principal and the 
interest is called the amount. 

Fill in the blanks below with the proper terms: 

1. $2000 is the amount borrowed by Mr. Elliott. It 

is called the_ 

2. One year is the _ for which the _ was bor¬ 

rowed. 

3. Six per cent is the-of interest paid on the_ 

4. $120 is the_on $_at-% for_ 

5. The amount is the_of the_and the-. 

The amount in this case was $- 

6. Money paid for the use of money is called_ 










132 


THE BAYNE-SYLVESTER ARITHMETIC 


96. Interest for One Year 

What is the interest on $720 for 1 year at 6%?^ 


A. 

B. 

$720 principal 

$7.20 ^ 

|726^X $43.20 interest 

.06 rate 

$43.20 interest 


Find the interest for one year on each of the following sums 


at the rates given: 

1. $500 at 6% 

2. $200 at 6% 

3. $1000 at 6% 


4. $800 at 4% 

5. $600 at 4% 

6. $300 at 6% 


7. $1200 at 5% 

8. $900 at 5% 

9. $700 at 4% 


97. Interest for More Than One Year 

Mr. Chambers borrowed $750 for 2 years, paying in¬ 
terest at the rate of 5%. How much would he pay in 
interest for the 2 years? 


A. 

$750 principal 
.05 rate 

$37.50 interest for 1 year 
_2 

$75.00 interest for 2 years 


B. 

$7.50 r 

2 = $75.00 
interest 


^ Unless otherwise stated, rates of interest in this book are to be regarded 
as annual rates. 








SEVENTH GRADE 133 

How do you find the interest for more than one 
year? 

Two important facts concerning interest for more than 
one year must be kept in mind. In the first place, we 
must remember that we must find the interest for one 
year before we can find the interest for a longer period. 
In the above example, Mr. Chambers paid interest on 
$750 at the rate of 5% per year for each of two years. If 
the money was kept for a longer period, Mr. Chambers 
would pay at the rate of 5% per year for each year’s use 
of the $750. 

In the second place, we must remember that interest 
on borrowed money must be paid at certain definite in¬ 
tervals. When money is borrowed for periods longer than 
a year, interest is usually paid at the end of each year or 
at the end of each six months. Banks require the pay¬ 
ment of interest at the end of every six months. 

1. Find the total amount of interest on each of the 
following sums: 


Principal 

Rate 

Time 

Principal 

Rate 

Time 

(a) 1350 

6% 

2 years 

id) 

$280 

4% 

3 years 

(6) $480 

6% 

3 years 

(e) 

$1200 

4% 

2 years 

(c) $1750 

6% 

3 years 

(/) 

$950 

5% 

2 years 

2. Mr. 

Chase 

borrowed 

$1500 at 

5% 

interest. 


(a) What was the annual interest on the loan? (6) If 
Mr. Chase kept the principal for 3 years, how much in¬ 
terest did he pay in all? 

3. A man borrowed $14,000 to invest in an orchard. 
The rate of interest was 5%. How much interest would 
be paid in all for 4 years’ use of the money? 


134 


THE BAYNE-SYLVESTER ARITHMETIC 


4. A schoolhouse in a small town cost $75,000. 
(a) At 4%, what is the yearly interest on this sum? 
(5) How much interest would be paid in all for 3 years? 

5. Mr. Platt borrowed $950 for 1 year from the Chat¬ 
ham Bank at 6% interest, (a) How much did he owe 
at the end of the year? (b) How much of this sum was 
interest? 

6. Fred Stone borrowed $550 at 6% and agreed to 
pay the bank $583 at the end of a year. How much of 
this sum was interest? 

98. Interest for Less Than One Year 

Mr. Jones borrows $650 from his bank for 6 months, 
paying interest at the rate of 6% for the use of the money. 
How much interest must he pay? 


A. 

B. 

$650 principal 

Q 

.06 rate 

$6.50 % 1 

2)$39.00 interest for 1 year 

^ = $19.50 

$19.50 interest for 6 

^ interest 

months 



How was the interest for 6 months found in A? In B 
we changed the rate to _ and the months to a frac¬ 
tional part of a year. Then we_the principal by the 

_and by the_ 

Without 'pencil. 

In the following examples, change the months to frac¬ 
tional parts of a 'year. Reduce fractions to lowest terms: 










SEVENTH GRADE 


135 


(a) 

(b) 

(c) 

id) 

(e) 

3 mo. 

2 mo. 

7 mo. 

4 mo. 

5 mo. 

11 mo. 

8 mo. 

9 mo. 

6 mo. 

10 mo. 


3. Find the interest for the sums indicated: 


Principal 

Rate 

Time 

Principal 

Rate 

Time 

(a) $300 

6% 

4 months 

id) 1800 

6% 

8 months 

(6) $500 

6% 

6 months 

(e) S600 

5% 

2 months 

(c) $400 

5% 

6 months 

(/) 1200 

4% 

9 months 


With 'pencil. 

4. If I borrow $250 for 8 months at 6%, how much 
interest must I pay? 

5. If I borrow $1200 for 9 months at 6%, what amount 
will I owe at the end of the 9 months? 

6. Mr. Ford obtained a loan of $480 from his bank at 
6% for 8 months. How much interest did he pay when 
the loan was due? 

7. A man borrowed $7500 to start in business. At 6%, 
how much interest would he pay each half-year? 

8. Compute the interest: 


Principal 

Rate 

Time 

Principal 

Rate 

Time 

(a) $4200 

6% 

6 months 

(e) 12100 

3% 

9 months 

(6) $2600 

4% 

6 months 

if) S3500 

4% 

9 months 

(c) $2000 

5% 

3 months 

iff) 11243 

6% 

8 months 

(d) $3800 

6% 

6 months 

ih) $3740 

5% 

2 months 


99. Interest for Years and Months 

Mr. Williams borrowed $460 at 6%. The loan was 
repaid at the end of 1 year and 6 months. How much 
interest did Mr. Williams pay on the loan? 


136 


THE BAYNE-SYLVESTER ARITHMETIC 


$4.60 g 3 

^ = S41.40 interest 


To find the interest for years and months, multiply 
the principal by the rate expressed as a fraction and 
by the time expressed as a fraction of a year. 


1. A man borrowed S1800 at 6%. The loan was repaid 
at the end of 2 years and 6 months. How much interest 
was paid on the loan? 

2. In order to build a house, Mr. Smith borrowed $8000 

at 4%. (a) How much interest must be paid annually 

on this loan? (h) How much will Mr. Smith pay as 
interest if he keeps the money for 2 years 3 months? 

3. Mr. Reid bought a house costing $18,000. He paid 

$5000 in cash. His bank loaned him the remainder, taking 
a mortgage on the house and charging interest at the rate 
of 6%. (a) How much interest was due each half-year? 

(h) How much interest would Mr. Reid pay on the loan 
in 3^ years? 

4. Compute the interest: 


Principal 

Rate 

Time 

(a) $1250 

6% 

years 

(6) $1700 

5% 

2 years 2 months 

(c) $2150 

4% 

3 years 6 months 

(d) $900 

6% 

2\ years 

(e) $400 

5% 

4 years 9 months 

(/) $1500 

6% 

2 years 4 months 




SEVENTH GRADE 


137 


100. General Problems in Interest 

Without 'pencil, 

1. What is the interest on $500 (a) for 1 year at 6%? 
(5) For 6 months at the same rate? 

2. What sum must be paid as interest on a loan of $200 

for 2 years (a) at 5%? (h) At 4%? 

3. What is the interest on $300 (a) for 6 months at 

b%? (p) For 4 months? (c) For 9 months? ’ 

4. Principal, $6000; time, 2 years; rate, 6%. What 
is the interest? 

With pencil. 

6. Mr. James borrowed $8500 from the First National 
Bank to build a house. How much interest is due on the 
loan every six months, the rate of interest being 6%? 

*6. Mr. Davis borrowed $5000 on February 1, at the 
rate of 6%. (a) How much interest was due on August 1 ? 

(5) How much interest did Mr. Davis pay if the loan 
ran for a period of 3| years? 

7. Mr. French loaned a friend $2500 for 9 months at 
6%. What amount did he receive when the loan was paid? 

8. A county sold bonds amounting to $250,000 to 
build new roads. The interest rate was 4%. How much 
interest was due every six months? 

*9. I borrowed $1250 on July 1, 1929, and paid back 
the sum with interest at 6% on January 1, 1930. What 
amount of money did I pay to settle the debt? 

10. The Gotham Bank loaned Mr. Peters $1500 for 
8 months at 6%. At the expiration of the time, Mr. 
Peters settled the loan with a check for $1560. Was that 
the correct amount? 


138 THE BAYNE-SYLVESTER ARITHMETIC 

11. William Andrews has $250 on deposit in the Dime 
Savings Bank, which pays interest at the rate of 4%. 
How much interest would be credited to William’s account 
at the end of 6 months? 

*12. Earl had $500 on deposit in the Colonial Savings 
Bank on January 1. On April 1, interest at the rate of 4% 
was added. How much did Earl then have to his credit 
at the bank? 

13. What amount must the borrower return: 

(a) On a loan of $9500 at 6%, for 6 months. 

(5) On a loan of $6540 at 4%, for 2 years. 

(c) On a loan of $1050 at 3%, for 2 years 3 months. 

(d) On a loan of $870 at 4%, for 3 years 4 months. 

(e) On a loan of $790 at 5%, for 3 years 6 months. 

If) On a loan of $1800 at 6%, for 1 year 4 months. 

101. Formula for Computing Interest 


To find the interest on any sum, multiply the 
principal by the rate expressed as a fraction and by 
the time expressed as years or part of a year. 


This rule is sometimes expressed as follows: 

interest = principal X rate X time 

Using the initial letters only, we have: 
i = p X r X t 

We can shorten this still further and write: 
i = prt 



SEVENTH GRADE 


139 


I = yrt is a short way of expressing the rule for interest. 
Let us apply the rule. 

Mr. Francis borrows $600 for 2 years at 4%. What is 
the total amount of interest to be paid for the use of the 
money? 


i = prt $6 


a 

Hence, prt = ^ 

Or, interest = $72 


p = $600 

r = 6% 
t = 2 years 


Write each of the following examples in a way that will 
show that you know how to use the rule i = prt. Then 
work the example. Thus, if one example read: ''Find 
the interest on $250 at 4% for 3 years, you would write: 


r 


V 


i = $250 X X 3 = ? 

1 . Compute the interest on $800 at 6% for 2 years. 

2. Compute the interest on $960 at 5% for 3 years. 

3. Find the interest to be paid on a loan of $450 at 6% 
for 2 years 6 months. 

4. I borrowed $500 at 6%. If I repaid the loan at the 
end of 1 year 8 months, how much interest was due? 

5. Mr. Parker borrowed $750 at 5% for 2 years 6 
months. What was the amount of the interest on the 
loan for the entire period? 

6. A business man borrowed $200 for 3 months at 
6% in order to take advantage of a large discount that 
was offered for cash payment of a bill. How much 
interest did he have to pay at the end of 3 months? 



140 


THK BAYNE-SYLVESTER ARITHMETIC 


102. Step-by-Step Test Drill. — Application of 
Percentage. I 




A 

B 

C 

D 

E 

1. 

Cost .... 

$12,000 

$16,000 

$2400 

$6250 

$5280 


Gain % ... 

10 

7 

12 

6 

5 


Gain .... 

? 

? 

? 

? 

? 

2. 

Cost . 

$6500 

$12,500 

$8250 

$7800 

$9550 


Loss % ... . 

12 

12 

6 

10 

15 


Selling Price 

? 

? 

? 

? 

? 

3. 

Amount of Sale 

$500 

$1500 

$9000 

$1200 

$1600 


Commission Rate . 

5% 

3% 

5% 

4% 

3% 


Commission 

? 

? 

? 

? 

? 

4. 

Amount of Sale 

$9000 

$7000 

$6000 

$5500 

$6256 


Commission % 

1 

8 

1 

4 

1 

2 

3 

4 

1 

8 


Commission 

? 

? 

? 

? 

? 

6. 

Selling Price 

$650 

$7500 

$1600 

$800 

$1200 


Commission Rate . 

4% 

8% 

2% 

5% 

3% 


Net Proceeds . 

? 

? 

? 

? 

? 

6. 

Cost .... 

$6000 

$3600 

$2500 

$10,000 

$20,000 


Gain .... 

$500 

$900 

$250 

$500 

$4000 


Gain % . . . 

? 

? 

? 

? 

? 


Amount of Sale 

$1200 

$1800 

$500 

$2500 

$3600 


Commission 

$100 

$90 

$20 

$50 

$300 


Commission Rate . 

? 

? 

? 

? 

? 

*8. 

Loss .... 

$600 

$250 

$375 

$800 

$900 


Loss % ... 

25 

50 

20 

33^ 

12i 


Cost .... 

? 

? 

? 

? 

? 

9. 

Commission 

$200 

$120 

$800 

$500 

$600 


Commission Rate . 

5% 

4% 

2% 

5% 

3% 


1 Amount Collected 

? 

? 

? 

? 

? 






























SEVENTH GRADE 


141 


103. Step-by-Step Test Drill — Application of 
Percentage. II 




A 

B 

C 

D 

E 

1. 

Principal 

$15,000 

$25,000 

$26,000 

$8000 

$12,000 


Rate 

8% 

6% 

5% 

7% 

5% 


Time 

1 yr. 

1 yr. 

1 yx. 

1 yr. 

1 yr. 


Interest 

? 

? 

? 

? 

? 

2. 

Principal 

$10,000 

$8500 

$7500 

$16,000 

$19,000 


Rate 

6% 

4% 

8% 

4% 

6% 


Time 

3 yr. 

3 yr. 

2 yr. 

4 yr. 

3 yr. 


Interest 

? 

? 

? 

? 

? 

3. 

Principal 

$6500 

$7200 

$8800 

$950 

$2100 


Rate 

7% 

5% 

6% 

6% 

4% 


Time 

9 mo. 

4 mo. 

6 mo. 

10 mo. 

8 mo. 


Interest 

? 

? 

? 

? 

? 

4. 

Principal 

$1750 

$8000 

$1500 

$5500 

$8600 


Rate 

4% 

6% 

5% 

6% 

3% 


Time 

25 ^. 6mo. 

lyr.9mo. 

lyr.4mo. 

2yr.6mo. 

7yr.8mo. 


Interest 

? 

? 

? 

? 

? 

6. 

Principal 

$6000 

$8000 

$7600 

$6200 

$6800 


Rate 

4i% 

5i% 

12i% 

3i% 

4i% 


Time 

2 yr. 

3 yr. 

2 yr. 

5 yr. 

4 yr. 


Amount 

? 

? 

? 

? 

? 

*6. 

Principal 

$1500 

$1800 

$7500 

$10,000 

$7500 


Rate 

? 

? 

? 

? 

? 


Interest 

$150 

$90 

$450 

$400 

$500 


Time 

1 yr. 

1 yr. 

1 yr. 

1 yr. 

1 yr. 

*7. 

Principal 

? 

? 

? 

? 

? 


Rate 

12i% 

10% 

4% 

4% 

5% 


Time 

1 yr. 

1 yr. 

1 yr. 

1 yr. 

1 yr. 


Interest 

$800 

$100 

$75 

$500 

$600 
























142 THE BAYNE-SYLVESTER ARITHMETIC 

104. Problem Analysis 

1. Before attempting to solve the problem, read it 
carefully. 

2. Ask yourself: 

(a) What facts are given? 

(b) What am I to find? 

(c) What is the first step? How shall I solve it? 

(d) What is the next step? How shall I solve that? 

(e) Are there any more steps? 

(/) What is a reasonable answer? 

3. Work the problem step by step. Check your 
answer. 

1 . A farmer’s wife sold 18 lb. of butter at the market. 
She received 42^^^ a pound. She bought 5 cans of corn at 
23^ a can and 2 bags of flour at $2.60 each. The remainder 
of the amount due her she took in cash. How much cash 
did she receive? 

2. Gasoline is selling at an average price of 22.5^ a 
gallon. Two years ago the average price was 18.5^. 
What would the increase amount to on 1200 gal.? 

3. It is 1052.7 mi. from Fort Worth to Chicago. How 
long will it take to make the trip on a train that averages 
48.4 mi. an hour? 

4. A one-way ticket by airplane between Boston and 
Newark costs $34.85. The round-trip ticket costs $64.70. 
What is saved by buying the round-trip ticket if you 
intend to return? 

5. A one-way ticket by air between New Orleans and 
Chicago costs $182. If the round-Trip ticket is 10% less 
than the single ticket each way, for what is it sold? 


SEVENTH GRADE 


143 


6. A plane leaving Fort Worth at 8 a.m. reaches 
Houston, which is 279 mi. distant, at 11 a.m. What is 
the average mileage per hour? 

7. The air-mail rate from Miami to Havana is 5^ for 
each half-ounce. How much postage is needed for a 
package weighing 8 oz.? 

*8. Mr. Martin bought an automobile for $1500. Two 
years later he traded it in for another car that cost $1850. 
He gave the dealer his old car and $1275. What per cent 
of the cost of the old car was he allowed? 

9. A clerk sold an article for $245. He billed the 
customer for $2.45. How much loss would this mean to 
the firm? 

10. Mr. Todd allows $500 a year for clothing for his 
family. This is 16% of his salary. What is his salary? 

11. How much will it cost to cement the floor of a 
cellar measuring 18 ft. by 22 ft. at $.60 a square foot? 

12. A six-passenger plane flying between Denver and 
El Paso carried 2 through passengers and 4 from Denver 
to Santa Fe. At Santa Fe 4 passengers were taken 
aboard, who completed the trip to El Paso, (a) What 
was paid in fare on this plane if a ticket from Denver to 
El Paso is $67.50, one from Denver to Santa Fe is $39, 
and one from Santa Fe to El Paso is $32.50? (5) How 
much more or less is this than the fare paid by 6 through 
passengers? 

13. At 16jz^ per 100 cu. ft. of water, what does the city 
receive for 25,650 cu. ft.? 

14. The wages for a plasterer in one year amounted 
to $2400. A carpenter earned $2000 the same year. 

(а) How much greater was the income of the plasterer? 

(б) What per cent was this of the carpenter’s income? 


144 


THE BAYNE-SYLVESTER ARITHMETIC 


105. Supplying the Question 

Example: Sarah paid $45.50 for a coat. Jane waited 
for the sales and bought a similar coat at a reduction of 
20 %. 

Possible questions to complete the example: 

(a) What did Jane pay for her coat? 

(b) How much less did Jane pay for her coat? 

(c) What part of the regular price was the reduction? 

Complete each problem by supplying a question. Then 
solve the problem: 

1. Mrs. Brown gave the butcher a five-dollar bill in 
payment for 8 lb. of ham at $.38 a pound. 

2. Mr. Dodd’s speedometer registered 6248.5 mi. 
when he started on his trip. At the end of the first day 
it registered 6426.2 mi. At the end of the second day it 
registered 6600.8 mi. 

3. An automobile traveled 28.2 mi. the first hour, 
25.4 mi. the second hour, and 26.5 mi. the third hour. 

4. Fred found that his car averaged 16.2 mi. to the 
gallon. Gasoline sells for $.22 a gallon. Fred used 
10 gal. 

5. A cubic foot of water weighs 62.5 lb. A cubic foot 
of ice weighs .92 times as much as a cubic foot of water. 

6. Three packages weighed as follows: 26J lb.; 18J 
lb.; 27f lb. 

7. A rug measures 8j ft. by 10^ ft. 

8. Anna paid $4.50 for 2| doz. favors for her party. 

9. Lester sold a bicycle that cost him $40 at a loss of 
30%. 

10. Mr. Thomas borrowed $1600 for 2 years at 5%. 


SEVENTH GRADE 


145 


106. Approximating Answers 

Example: A real-estate agent sold a house for a client 
for $12,500. He charged the owner 4%. What was his 
commission? 

$400 $500 $125 $600 

Think: 1% = $125 4% = 4 X $125 = $500 

In the following problems you are to select from the four 
answers the one which is right: 

1. A suit was bought at a sale for $48. This was 80% 
of the regular price. Wliat was the regular price? 

$60 $75 $70 $50 

2. Mrs. Field bought 3 blankets at a sale. They were 
marked down ^ from the regular price, which was $9 each. 
What did she pay for them? 

$27 $18 $12 $6 

3. A dealer sold 150 T. of coal at $14.50 a ton and 150 
T. at $15 a ton. What did he receive for the coal? 

$4200 $4800 $4425 $2250 

4. The distance between two cities is 625.6 mi. If it 
takes a train 16 hr. to make the trip, what is the average 
mileage per hour? 

41.5 mi. 400 mi. 25 mi. 39.1 mi. 

6. A man’s wages amounted to $44 for 5| days’ work. 
What was his average daily wage? 

$10 $9 $22 $8 


146 


THE BAYNE-SYLVESTER ARITHMETIC 


107. Selecting the Operation 

Select the right solution from the three suggested and write 
it after the number of the problem on a sheet of paper: 

1. A man bought a horse for $175 and sold it for 20% 
less than he paid for it. What was the selling price? 

$175 - $20 i of $175 $175 - (20% of $175) 

2. A man bought milk for 40 a gallon and sold it at 
15j^ a quart. What was the rate of gain? 

if = I = 37i% (4 X $.15) - $.40, = 50% 

$.40 + .15 = 55% 

3. At 90^ a pound, what will 8 oz. of tea cost? 

$.90 -r- 8 8 X $.90 J of $.90 

4. John raised 500 chickens. He sold 75% of them to 
the butcher. How many had he left? 

75 X 500 f X 500 J X 500 

5. Find the cost of 5500 lb. of hay at $22 a ton. 

5000 X $22 2f X $22 5 X $22 

6. Mr. Sims sold some hay at the rate of $20 a ton. 
His bill was $70. How many tons did he sell? 

$20 $70 $20 X $70 $70 $20 

7. What will 15,000 shingles cost at $6 per thousand? 

15,000 X $6 15 X $6 150 X $6 

8 . What is the average mileage per gallon of gasoline if 
one can travel 162.5 mi. on 10 gal.? 

10 X 162.5 162.5 - 10 


162.5 -J- 10 


SEVENTH GRADE 


147 


108. Changing the Wording of Problems 

Example: A dealer bought an article for $75. He was 
forced to sell it for $60. What was the per cent of loss? 

(a) An article that is bought for $75 and sold for $60 is 
sold at a loss of_%. 

(5) What is the per cent of loss on an article which is 
purchased for $75 and sold for $60? 

Vary the wording of the following problems in as many 
ways as possible: 

1. Mr. Ellis paid $2400 for an automobile which he 
sold at a loss of 25%. What was his loss? 

2. At a clearance sale an article marked $50 was sold 
for $25. What was the per cent reduction? 

3. How many square feet are there in a plot of ground 
28.5 ft. long and 24.6 ft. wide? 

4. A motor boat which averages 28.4 mi. an hour will 

travel_miles in 6 hr. if it continues at the same rate. 

5. John had 18 examples right out of 25. What per 
cent should he receive? 

6. Alice finds that her car averages 12.8 mi. to the 
gallon of gasoline. How far will she travel on 10 gal.? 

7. A farmer sold half his crop of potatoes in the fall 
at $1.75 a bushel. He held the remainder until spring 
and had to sell at $1.40 a bushel. What was the rate of 
loss through holding his crop? 

8. What is the rate of commission on a sale amounting 
to $2500 if the agent’s fee is $250? 

9. Find the interest on a loan of $16,500 at 6% for 
12 months. 



148 


THE BAYNE-SYLVESTER ARITHMETIC 


109. Problems without Numbers 

In each of the following, tell how you would solve the 
problem. Then supply reasonable figures for the missing 
numbers and find the answer: 

1. Mr. Miller bought a house for_He spent- 

for repairs and then sold the house for-What was 

the per cent gain? 

2. 'WTiat must James pay for a railroad ticket if the 

distance is_miles and the cost-per mile? 

3. A merchant sold a coat that cost-so as to gain 

_%. What was the selling price? 

4. Mr. Weed borrowed_for-years at-%. 

What did he pay in interest? 

5. A man sells goods on commission. He charges 

_%. What will he receive if the sales amount to_? 

6. What must he pay for_ cubic feet of gas at 

$1.20 per thousand? 

7. William earned_while in college. His expenses 

amounted to_What per cent of his expenses did he 

earn? 

8. An agent received_for selling a house. This 

amounted to_% of the selling price. What was the 

selling price? 

9. On a recent automobile trip Mr. Williams averaged 

_miles per hour. How long did it take him to travel 

_miles? 

10. Mary left the Grand Central Station at_and 

reached her destination at_If the average speed of 

the train was_miles per hour, how far did she travel? 






SEVENTH GRADE 


149 


110. Silent Reading of Problems 

After each 'problem 'you 'will fi'nd a question followed by 
four answers. Select the correct answer: 

1. Which is cheaper: to buy 50 lb. of sugar in five- 
pound cartons at each, or to buy a fifty-pound sack 
for $2.50? How much cheaper is it per pound? 

Which of the following facts are given? 

(a) The cost per pound of si^ar. 

(5) The number of cartons. 

(c) The price of a fifty-pound sack. 

(d) The difference in price per pound. 

2. It takes Dan 12| sec. to run the 100-yard dash. 
Bob can run it in 12| sec. How much faster is Bob’s 
time than Dan’s? 

Which of the following are you asked to find? 

(a) The difference in time. 

(b) The average time. 

(c) The total distance run by the two boys. 

(d) The total time made by the two boys. 

3. Mr. Davis bought gasoline at a service station last 
year at an average price of 22.5^ a gallon. This year the 
average price is 24.2^. How much difference will this 
make in the expense of running a car if he uses 275 gal.? 

Which of the following are you asked to find? 

(a) The difference in cost per gallon. 

(b) The average mileage per gallon. 

(c) The cost per year. 

(d) The difference in cost for 275 gal. 


150 THE BAYNE-SYLVESTER ARITHMETIC 

4. Mary picked berries in the summer to earn money. 
She sold 3 crates containing 24 quart boxes each at 18^ a 
quart. What price did she get for her berries? 

Which of the following facts are given? 

(а) The number of quart boxes she sold. 

(б) The selling price of a quart box. 

(c) The cost per crate. 

{d) The time she worked. 

6. Canned peaches sell regularly at 29a can and 3 for 
70^ at a sale. How much do you save by buying 3 cans at 
the sale rather than one can at three different times? 

Which of the following are you asked to find? 

(a) The cost of 3 cans bought one at a time. 

(5) The cost per can when bought at a sale. 

(c) The saving on 3 cans when bought at a sale. 

(d) The cost of 6 cans. 

6. Jack’s father needs 2 new tires for his truck. The 
regular price is $36 a tire with a discount of 15% for cash. 
What will the tires cost him? 

Which of the following facts are given? 

(a) The price paid by Jack’s father. 

(5) The cost of 2 tires. 

(c) The selling price of the tires. 

^ (d) The rate of discount allowed for cash. 

111. Our Ball Team 

Public School 50 is very proud of its baseball team. It 
has played 10 games this year and has lost only 2 games. 
The boys and girls have computed the per cent of games 
won as follows: 


SEVENTH GRADE 


151 


You see how easy it 
is to figure this out. 
It is just the second 
case of percentage. 

Public School 44 has played 9 games and won 6. Its 
standing is f = 66|% = .66|. 

In a newspaper the ^‘Standing of the Clubs’’ is carried 
out to three decimal places; any fractions remaining are 
dropped. Public School 44 would rank thus: .666. 
Public School 50 would rank .800. When we express 
athletic standing in three decimal places, it isn’t really a 
^^per cent” although many newspapers call it that. 

112. Problems 


1 . Our school league standing ended as follows: 


Lincoln .... 

Played 

12 

Won 

8 

Lost 

4 

Garfield .... 

10 

4 

6 

Roosevelt . 

12 

6 

6 

McKinley . 

10 

6 

4 

Washington 

12 

4 

8 

Calculate the standing 

of each team and 

arrange 


teams according to their standing, the highest one first. 

2. The final standing of the 8 National League teams 


in 1927 was as follows: 



Won 

Lost 


Won 

Lost 

Pittsburgh . 

. 94 

60 

New York 

. 92 

62 

St. Louis 

. 92 

61 

Brooklyn . 

. 65 

88 

Philadelphia 

. 51 

103 

Cincinnati 

. 75 

78 

Boston . 

. 60 

94 

Chicago . 

. 85 

68 


Calculate the standing of each team and arrange the 
teams according to their standing, the highest one first. 


games won 8 ^ g 
games played 10 





152 


THE BAYNE-SYLVESTER ARITHMETIC 


113. Studying a Time-Table 

This time-table shows a section of the time-table or 
schedule under which trains are running from Chicago to 
points West. 


No. INo. 19 

Dail” 1 Daily 

No. 13 

Daily 

Miles 

Table 9 

No. 8 

Daily 

No. 14 

Daily 

No. 3 

Daily 

No. 34 

Daily 

3 3J 

AM 

9.40 

AM 

5.40 
f 6.10 
f 6.20 
f 6.35 
f 6.52 
7.02 
f 7.10 
f 7.37 
f 7.53 
f 8.04 
* 8.15 

991.2 

1008.8 

1014.4 

1022.3 

1031.7 

1036.3 
1040.9 

1054.7 
1062.6 

1068.7 
1073.0 

Mountain Time 

Lv. .LA JUNTA 3, 4, 5. . Ar 
Lv.Timpas.Ar 

PM 
4.10 
f 3.40 
f 3.30 
f 3.18 

PM 
9.00 
8.36 
f 8.17 
f 8.04 
f 7.49 
f 7.41 
f 7.33 
f 7.13 
6.57 
f 6.48 
6.40 

AM 

1.50 

AM 

3.35 



Lv.Ayer.Ar 





Lv.Bloom.Ar 





Lv.West.Ar 





Lv.Thatcher.Ar 

f 3.56 
f 3.48 





Lv.Simpson.Ar 





Lv.Earl.Ar 





Lv.Hoehnes.Ar 

f 3.14 





Lv.El Moro.Ar 



*5 35 

11.40 

Ar.TRINIDAD . . . . Lv 

1.55 

11.45 

1.20 


Note that in this time-table the mileage at La Junta is 
given as 991.2. This is the distance of La Junta from 
Chicago. If the mileage had been reckoned from La 
Junta, it would read 0.0. 

If you are going from La Junta to Trinidad, read down 
the section of the time-table at the left. If you are travel¬ 
ing from Trinidad to La Junta, read up the section at the 
right. What does a.m. mean? What does p.m. mean? 

1. How many trains leave La Junta during the day? 
Which one leaves earliest? Which is the last train out of 
La Junta? 

2. If you want to get to Trinidad a little before noon 
which train should you take? 

3. Which are express trains? Which are local? 

4. The ‘T” before the local stop means ^^flag stop.'" 
What is a “flag stop”? 

5. How long does it take to get to Trinidad on the 
local train? 





















































SEVENTH GRADE 


153 


6. How many trains arrive in La Junta during the 
day? 

7. Which train makes the best time from Trinidad to 
La Junta? 

8. William wishes to go from Trinidad to West. 
Which train must he take? Why? 

9. How far is Trinidad from La Junta? 

10. Nellie got on the train at Simpson. She was going 
to Trinidad. At $.035 a mile, what did she have to pay 
for her ticket? 


114. Traveling by Airplane 

The first settlers in America came to these shores in 
sailboats. People of Revolutionary times traveled by 
stage or coach. Then in turn came the steamboat, the 
steam engine, the automobile, the great ocean liners, and 
the airplane. 

You know, of course, that sending mail by air is a 
regular part of the United States Postal System. 

Did you know that regular travel service through the 
air is so general that the companies have time-tables show¬ 
ing time, distance, and connections between cities all over 
the United States and the West Indies? 


NORTHBOUND Twelve-Passenger SOUTHBOUND 

Read Down Multi-Motored Cabin Planes Read Up 

Daily 

Ex. 

Sun. 

Daily 

Miles 

TABLE 16 

Pacific Standard Time 

Daily 

Ex. 

Sun. 

Daily 

AM 

9.00 

S « 

5 t 

12.00 

M 

AM 

10.00 

11.00 

11.00 

12.00 

PM 

4.00 

5.00 

5.15 

0 

110 

110 

220 

370 

380 

Lv Los Angeles (Gd. Cen. Air 
Term.) Ar 

T.v .Eresno.Lv 

AM 

10.45 

9.45 

9.40 

PM 

1.45 

12.45 

12.45 

11.45 

PM 

6.15 

0 » 

S- 'S 

A t 

^ QC 

3.15 
PM 

Ar Oakland Municipal Airport.. . . 


7.45 

Ar. Alameda Airport .Lv 

7.20 

AM 

10.15 

AM 

1.30 

PM 

PM 




























154 


THE BAYNE-SYLVESTER ARITHMETIC 


On page 153 is a time-table of one of the air lines. 
Notice that it is like the railroad time-table except that 
the distances between cities are much greater. 

1. In which direction will you read going from Los 
Angeles to Alameda? Why? 

2. In which direction will you read going from 
Alameda to Los Angeles? Why? 

3. How many planes leave Los Angeles in the morn¬ 
ing? How many leave in the afternoon? 

4. How many planes leave Alameda for Los Angeles 
during the day? 

5. Which plane leaving Alameda reaches Los Angeles 
before noon? 

6. What does Thru Service’^ mean? 

7. How many express planes are there in each direction? 

8. What is the distance between Alameda and Los 
Angeles? 

9. How far is it to Fresno from Los Angeles? From 
Fresno to Alameda? 

10. How long does it take to go from Los Angeles to 
Alameda by the plane leaving at 9 a.m.? 

11. Which northbound plane stops at Bakersfield for 
a quarter of an hour? 

12. Find the length of time it takes each plane to make 
the trip from Alameda to Los Angeles. 

13. Find the mileage per hour for each plane. 

14. The plane leaving Los Angeles for Alameda at 
10 A.M. carried 5 through passengers who paid a fare oi 
$32.50 each. It carried 7 passengers to Fresno who paid 
$20 each. At Fresno it took on 7 passengers for Alameda 
who paid $15 each. What was the total fare collected on 
this trip? 


SEVENTH GRADE 


155 


116. Problems on Airplane Travel 

1 . An airplane leaving Cleveland at 12.30 p.m. reaches 
Washington at 3.30 p.m. (a) How long does it take to 
make the trip? (b) What is the average mileage per 
hour if the distance is 236 mi.? 

2. A plane leaving Oakland at 4.45 p.m. reached San 
Jose at 5.10 p.m. The distance is 40 mi. (a) What is 
the average speed per minute? (b) What would be the 
average hourly speed? 

3. (a) Mr. Perkins left Boston by airplane at 4 p.m. 
and reached Newark at 6 p.m., a distance of 201 mi. 
What was the average mileage per hour? (b) His ticket 
one way cost $34.85. What was the average cost per 
mile? (2 decimal places.) 


SOUTHBOUND Eight-Passenger Cabin Planes NORTHBOUND 

Read Down Read Up 

Daily 

Miles 

TABLE 10 

Central Standard Time 

Daily 

9.00 AM 
11.56 AM 
13.23 PM 
3.17 PM 

0 

252 

Lv. Chicago .Ar 

Lv.St. Louis.Ar 

3.58 PM 
13.03 PM 
11.40 AM 
9.00 AM 

500 

Ar. Memphis .Lv 


4. Mrs. Graham studied this time-table to find how 
long it would take her to make the trip from Chicago to 
Memphis, (a) At what time would she leave Chicago 
(6) When would she reach Memphis? (c) How long 
would it take her? (d) What distance would she travel? 
(e) How long would she stop at St. Louis? 

5. What is the average mileage per hour of the plane 
in which Mrs. Graham intended to travel? (2 decimal 
places) 

6. Make up another problem about a trip from Mem¬ 
phis to Chicago. 


















156 


THE BAYNE-SYLVESTER ARITHMETIC 


7. (a) The distance by airplane between Toronto, 
Canada, and Buffalo, New York, is 100 mi. At $15 for 
a one-way ticket, what is the cost per mile? (b) A round- 
trip ticket costs $25. How much is saved by purchasing 
a round-trip ticket? (c) What is the cost per mile at the 
lesser rate? 

8. Mr. Roberts left New York for Montreal by airplane 
at 7 A.M. He reached his destination at 11.15 a.m. (a) 
How long did it take him to make this 334-mile trip? 
(b) What was the average mileage per hour? 

116. Using a Ticket Schedule 

John^s father is a clerk in the ticket office of an airplane 
company which runs a fleet of planes between Albany 
and Cleveland. 


One-Way Between 

Cleveland 

Buffalo 

Rochester 

Syracuse 

Utica 

Schenectady 


$25.00 

32.00 

43.00 

50.00 

55.00 

60.00 







$15.00 

25.00 

30.00 

35.00 

40.00 






$15.00 

25.00 

30.00 

35.00 




Utica-Rome. 

Schenectady. 

Albany . 

$15.00 

25.00 

30.00 

$15.00 

20.00 

$7.00 


This is the schedule on which he bases the charge to 
passengers. Notice that the schedule gives the fare 
between cities. 

John wished to learn how to read the schedules. His 
father explained it as follows: 

Today a passenger wished to go from Schenectady to 
Cleveland. I charged him $55. If I hadn’t known the 
rate, I would have looked down the left-hand column 
for Schenectady and then across until I came to the 
vertical column with Cleveland at the top.” 





















SEVENTH GRADE 


157 


He then asked John to find the fare between Schenec¬ 
tady and Utica. John said $15. Was he right? 

‘^Now try to find the fare between Schenectady and 
Albany.’’ 

John tried to find it as he had the other but could not 
because there was no vertical column headed “Albany.” 

1. Can you find the answer to John’s problem? 

2. Find the cost of a one-way ticket (a) between Buffalo 
and Cleveland; (b) between Rome and Rochester; (c) 
between Albany and Syracuse; (d) between Rochester 
and Syracuse. 

3. Plane A accommodates 6 passengers. What will be 
the revenue from this plane if it is loaded to capacity with 
passengers making the trip from Albany to Cleveland? 

*4. Plane B is also a six-passenger plane. It carried 
4 passengers from Albany to Buffalo, 2 from Albany to 
Cleveland, and 4 from Buffalo to Cleveland, (a) How 
many passengers alighted from the plane at Cleveland? 
(h) Which plane, A or B, earned more in fares? (c) How 
much more did it earn? 

117. Parcel Post 

While Henry and his mother were in the country this 
summer, they learned to like the farm and the good food 
they had. Henry’s mother thought it would be fine if 
they could have fresh eggs from the farm all winter 
through. Henry couldn’t see how the farmer could get 
the eggs to them except by sending them to their grocer 
in New York. But the farmer laughed and showed him 
a little metal box just large enough to hold a dozen eggs. 
He told Henry that he could send the eggs in the box by 


158 


THE BAYNE-SYLVESTER ARITHMETIC 


mail. In this way Henry learned that the United States 
Government has a way of sending packages by mail. 
This is called the Parcel Post System. Mail sent in this 
way is ranked as fourth-class mail. The farmer explained 
that the government charges for the weight of the package 
and for the distance it is carried. The rates are as follows: 


Zones 

Distance First Pound 

Additional Pounds 

Local 



1 ^ for each 2 pounds 

1 

Up to 50 miles 

7(< 

lf!f for each pound 

2 

50 to 150 miles 


1 ^ for each pound 

3 

150 to 300 miles 

H 

2<^ for each pound 

4 

300 to 600 miles 

H 

4^ for each pound 

5 

600 to 1000 miles 

H 

6^ for each pound 

6 

1000 to 1400 miles 

lOf' 

8^!f for each pound 

7 

1400 to 1800 miles 

\2i 

lOj^ for each pound 

8 

Over 1800 miles 


12^ for each pound 


Limit of size: 84 inches in length and girth combined. 

Limit of weight: 70 pounds in Zones 1, 2, and 3 and 50 
pounds in all others. A fraction of a pound is counted as 
another pound. 

Insurance rates: For a valuation up to and not exceed¬ 
ing $5, the fee is 5|^; above $5 and not over $25, 8^; above 
$25 and not over $50, lOf!^; above $50 and not over $100, 
25 ^. 

Return receipts for domestic insured parcels may be 
obtained upon request and payment of for each 
receipt. 

The farmer told Henry’s mother that he would supply 
eggs through the year by parcel post at 50^ a dozen if 
she would pay mailing charges. Henry decided to find 
what this would cost. He got a map and calculated that 


SEVENTH GRADE 


159 


the farm was 80 miles from his home. He found that the 
case weighed half a pound and the eggs pounds. The 
postage was therefore 8 cents. This is the way in which 
he found it: 


Weight of case and 

Rate for first pound 

= 

eggs = 2 lb. 

Rate for second pound 

= H 


Total 

H 


1. A parcel weighing 10 lb. was sent to Zone 4. What 
was the postage? 

2. A box weighing 25 lb. was sent to Zone 3. What 
was the postage? 

3. What was total cost of sending a package weighing 
18 lb. to Zone 5, if it was insured for S25? 

4. A merchant sends 12 pkg. weighing 4 lb. each to 
Zone 2. He insures each package for $10. What will the 
entire shipment cost him? 

6. Henry sends a box weighing 4 lb. to a friend 1200 
miles away. He insures the box for $12. What are his 
total mailing charges? 

6. A mail-order house sends its goods by parcel post. 
Find the total cost of postage and insurance on each of 
the following shipments: 


Number of Packages 

Weight 

Value 

Zone 

72 

5 lb. each 

$10 

2 

15 

12 lb. each 

$25 

4 

140 

8 lb. each 

$50 

5 

43 

27 lb. each 

$25 

3 

164 

16 lb. each 

$100 

1 



160 


THE BAYNE-SYLVESTER ARITHMETIC 


118. How to Send Money 

Henry’s mother decided to pay the farmer every four 
weeks for the fresh eggs which she got from him weekly. 
Since the farmer had agreed to charge 50 a dozen for 
the eggs all winter, $2.00 for eggs and 32for postage had 
to be sent him every four weeks. Because his mother had 
no bank account, Henry wondered how the farmer would 
get the money. His mother could, of course, send the 
money in an envelope, but it might easily be lost. His 
mother then explained that the United States Govern¬ 
ment offers a way to send money by mail. Money orders 
are purchased by the sender at a rate varying with the 
amount. You go to the post office and fill out a blank, 
handing it to the clerk with the money to be sent. The 
clerk then gives you an order on the postmaster of the 
town to which the money is to go. This order shows the 
name of the person to whom the money is to be paid. 
You then mail the order to that person. When he re¬ 
ceives it, he takes it to his post office and obtains the 
amount indicated. 

No money order may be made for more than $100. 
What would you do if you wanted to send $150? 

The fees or charges for money orders are as follows: 


Amount 

Fee 

Amount 

Fee 

Up to $2.50 

H 

$20.01 to $40.00 

IH 

$2.51 to $5.00 

7(4 

$40.01 to $60.00 

IH 

$5.01 to $10.00 

10(4 

$60.01 to $80.00 

20(4 

$10.01 to $20.00 

12?! 

$80.01 to $100.00 

22(4 


From this table you can see that it cost Henry’s mother 
5^ a month to pay for the money order she was sending. 


SEVENTH GRADE 


161 


119. Problems 

Without pencil. 

How much will a postal money order for each of the 
following amounts cost? (Cost = amount of order + 
fee.) 

1. $2.50 3. $25 5. $96 7. $82 9. $43.25 

2. $2.75 4. $70 6. $79 8. $17.50 10. $68.40 

With pencil. 

11. What postal money orders would you buy, and 

what would be the fee for sending (a) $130.50? (5) 

$209.85? (c) $149.80? 

12. A man buys money orders for $50, $85, $25.20, 
$75, and $46. How much would he save by sending 
checks for these amounts? 

*13. If you had to send $110 by money order, which 
would be cheaper: (a) to buy 2 orders for $100 and $10, 
or {h) to buy 2 orders for $55 each? 

120. Right Angles and Rectangles 

Most objects with which we deal in a schoolroom, such 
as books, paper, tops of desks, blackboards, doors, and 
windows, have four square corners. They are shaped like 
this: 


We call such forms rectangles. The square corners 
are called right angles. Unless the four angles are right 




162 


THE BAYNE-SYLVESTER ARITHMETIC 


angles, the figure is not a rectangle. If the 
four sides of the figure are equal, it is called a 
square. A square is a rectangle that has four 
equal sides. 

The area of a rectangle is easy to determine. Here is 
one 5 units long by 2 units wide. You can see from the 
diagram that there are 5 square units in each row and 

that there are 2 rows of such units. ----- 

Therefore, the area of this rectangle_ 

is 10 square units (2X5 square 
units = 10 square units). The area 

of any rectangle is equal to the number of units in its 
length multiplied by the number of units in its width. 

Area = length X width 

The length is also known as the base of the rectangle, 
and the width is also known as the height; we may there¬ 
fore say that 

Area = base X height 

or, using letters, 

A = b X h 

(Learn to use letters in expressing your formulas or 
ways of doing arithmetical processes. It will help you 
in your work later.) 


Find the area, in square feet, of rectangles having the 


following dimensions: 

1. 12 ft. by 15 ft. 

2. 43 ft. by 36 ft. 

3. 25 ft. by 40 ft. 

4. 56' X 20' 

6. 17' X 29' 


6. 16'6" X 32'8" 

7. 45 ft. by 15 ft. 4 in. 

8. 35 ft. by 24 ft. 

9. 5 = 12 ft.; /i = 6J ft. 

10. 5 = 37 ft.; = 96 ft. 









SEVENTH GRADE 


163 


121. Area of a Right Triangle 

Here we have a rectangle with a height of 4 units and 
a base of 6 units. Its area is 24 square units because 

6 X = A, or 6 X 4 = 24. 


4 


A D 

If we draw a diagonal line from A to C, dividing the 
rectangle into two parts, so that it looks like this, and 

B C 



place one of these parts on top of the other, matching 
the sides and angles, we shall find that the two parts are 
equal. 

Each one is one-half of the rectangle, and each therefore 
has an area of 12 square units. 

Note carefully these new names 
for the sides: 

The side AD is called the base. 

The side CD is called the height 
or altitude. 

The three-sided figure is called a triangle, and because 
it has one square corner, or right angle, it is called a right 









THE BAYNE-SYLVESTER ARITHMETIC 


164 


triangle. Its area is equal to one-half the product of the 
number of units of length in the base by the number of 
units of length in the altitude. 

Area of a triangle = ^ of (base X altitude) or A = —^— 


Find the area of triangles having the following dimen¬ 


sions : 

1. h = 9 yd.; a = 3 yd. 

2. 6=150 yd.; a = 79 yd. 

3. 6 = 225yd.;a = 64yd. 

4. b = 20i ft.; a=16 ft. 


5. 6 = 30f yd. ; a = 66 yd. 

6. 6 = 210 ft.; a = 96 ft. 

7. 6=12 ft. 9 in.; a =15 ft. 

8. 6 = 7yd.2ft.;a = 3yd.lft. 


122. Keeping a Record of Progress 


Walter finds that if he keeps a record of his progress 
he works much harder. 


September 

123456789 

% 

100 
95 
90 
85 

% 

100 
95 
90 
85 

% 

100 
95 
90 
85 















/ 



7 



\ 

/ 













October 











\ 

/ 




\ 

/ 


















November 














\ 

/ 




















In the front of his spelling 
book he keeps a graph on 
which he records the per cent 
he gets in each lesson. 

This diagram shows his 
record for three months for 
nine lessons. Notice that each 
month starts a new record. 
His aim is to keep a straight 
fine at the 100% mark. At 
the left side in the vertical 
column he has listed the per 
cents. On the horizontal line 
at the top he has placed the 
number of each lesson. To 
draw the line of progress for 
September, Walter said that: 




































SEVENTH GRADE 165 

(1) He found the horizontal line showing the per-cent 
rating. 

(2) He found the vertical line with the lesson number. 

(3) He placed a dot where these lines crossed to show 
his standing for the first lesson. 

(4) For the second lesson he found the per cent on the 
horizontal line. 

(5) Then he found vertical line for the second lesson. 

(6) At the place where the per-cent line crossed the 
lesson line he placed a dot. 

(7) Then he connected the dot at 90% with the one 
at 95%. 

(8) Each day after that he located the per cent on the 
lesson line and connected the new point with the preceding 
lesson. 

1. Study the part of each graph that is shown and 
answer these questions: 

(a) What was Walter’s lowest rating? 

(b) When did he receive it? 

(c) For how many lessons in September had he 

100 %? 

(d) For how many lessons had he 95% in October? 

(e) On which lesson did he drop to 95% in No¬ 

vember? 

(/) In which month does the graph show the best 
work? 

2. What kind of graph did Walter use to show his 
progress? 

3. Should you like to keep a graph similar to this to 
show your progress in some subject? Try it. You’ll be 
interested in seeing yourself improve, just as Walter did. 


166 


THE BAYNE-SYLVESTER ARITHMETIC 


123. Using the Bar Graph in Geography 

Often we wish, to make comparisons between countries 
in our study of geography. We can read figures and get 
the desired information, but if we can make a picture 
showing the relationship, we understand it better and we 
can make others understand it better. 

If you know how to make a bar graph, you can make 
such a picture. Let us suppose that we wish to show that 
immigration to the United States from certain countries 
in 1927 was as follows: 


Immigrants 


Country 

Great Britain 
France 
Germany 
Italy 


80,000 

10,000 

28,000 

35,000 


First of all, we must decide upon the scale to which the 
bars are to be drawn. For this graph, let us allow a 
quarter of an inch for each 10,000 persons. Using this 
scale, the lengths of the bars representing the various 
countries will be as follows: 


France 


Great Britain 


Germany 


Italy 








SEVENTH GRADE 


167 


The completed graph will then look like this: 


Great Britain 


France 


Germany 


Italy 


1. Make a bar graph comparing the populations of the 
following cities. Expressed in round numbers, the popu¬ 
lations are: 

New York 6,000,000 Berlin 4,000,000 

London 7,500,000 Vienna 2,000,000 

Paris 3,000,000 

Represent 1,000,000 population by a bar J in. long. 

2. The area of New York State is about 50,000 sq. mi. 
Construct a bar graph comparing it with the areas of the 
following countries, which are approximately: 

Great Britain 120,000 sq. mi. 

Germany 180,000 sq. mi. 

France 210,000 sq. mi. 

Italy 120,000 sq. mi. 

Use a bar 1 in. long to represent the area of New York 
State. 


■ 




■ 

s 

* 










































■ 


■ 

1 







Scale: >4" = 10,000 persons 


















168 


THE BAYNE-SYLVESTER ARITHMETIC 


3. Construct a bar graph to show the value of exports 
from the United States to certain European countries, 
using the following figures: 

Great Britain $900,000,000 
France $280,000,000 

Germany $380,000,000 
Italy $175,000,000 

4. Construct a bar graph to show the relative value of 
the exports of the following countries to the United States: 


Great Britain $350,000,000 
France $150,000,000 

Germany $150,000,000 


5. Illustrate with a bar graph the coal production of the 
following countries: 


United States 650,000,000 T. 
Great Britain 309,000,000 T. 
France 42,000,000 T. 

Germany 200,000,000 T. 


6. Using a bar graph, compare the populations of the 
following cities: 


Shanghai 1,500,000 

Peiping 1,300,000 

Calcutta 1,200,000 

Tokyo 2,100,000 

Vladivostock 100,000 


Alexandria 440,000 
Cairo 800,000 

Cape Town 210,000 
Algiers 210,000 

Tangiers 50,000 


7. From your geography get information that will 
enable you to compare the populations of the following 
countries: Japan, China, India, Turkey. 

8. Compare graphically the areas of China, Japan, 
India, and Turkey. 


SEVENTH GRADE 


169 


124. Standard Weights of a BusheD 


Wheat 60 lb. 

Com 56 lb. 

Barley 48 lb. 

Oats 32 lb. 


Potatoes 60 lb. 

Beans 60 lb. 

Rice 45 lb. 

Alfalfa 60 lb. 


Use pencil if needed. 

1. If potatoes are selling at $1.25 for a hundred-pound 
sack, what is a bushel worth? 

2. A farmer shipped a carload of wheat amounting to 
42,000 lb. (a) How many bushels did he ship? (5) What 
was the wheat worth at $1.10 a bushel? 

3. Find the cost of 300 lb. of potatoes at $.75 a bushel. 

4. How heavy is a load of 500 bu. of barley? 

5. (a) Which weighs more: 500 bu. of barley or 
400 bu. of rice? (6) How much more does it weigh? 

6. Find the cost of: 

(a) 4800 lb. of barley at $.73 a bushel. 

(5) 24,000 lb. of wheat at $1.15 a bushel. 

(c) 56,000 lb. of corn at $.74 a bushel. 

(d) 2820 lb. of potatoes at $.95 a bushel. 

(e) 88,000 lb. of oats at $.49 a bushel. 

7. How many bushels of wheat can be loaded on a 
freight car that has a capacity of 30 T.? 

8. (a) Which weighs more: 1600 bu. of rice or 1200 
bu. of alfalfa? (5) How much more does it weigh? 

9. A barrel of flour weighs 196 lb. (a) How much 
does i bbl. weigh? (5) J bbl.? (c) f bbl.? 

10. Make up a problem using the information given in 
the table of weights at the beginning of this section. 

1 Adopted by most states because of the varying weights of grain. 


170 


THE BAYNE-SYLVESTER ARITHMETIC 


125. Denominate Number Race 

Can you score 100% on this test? Compete row against 
row. The score is the number right. The row having 
the highest average score wins. 

Supply the missing numbers: 

A B 


1 . 15 dimes = $_ _hr. = 40 min. 


2 . 

yr. = 

10 mo. 

half-pints = 2 qt. 

3 . 

85 gal. = 

qt. 

.25 mi. = rd. 

4 . 

da. = 

1 leap year 

mills = 1 dime 

5 . 

3.25 ft. = _ 

in. 

48 hr. =_da. 

6 . 

.75 T. = 

lb. 

$1 = nickels 

7 . 

1 cent = 

mills 

5 cwt. = lb. 

8 . 

2 yr. 3 mo. 

= yr. 

hr. = 15 min. 

9. 

rd. = 

.5 mi. 

320 rd. = mi. 

10 . 

min. = 

= 20 sec. 

qt. = .5 gal. 

11 . 

5 mi. = 

yd. 

Ij gross = doz. 

12 . 

sq. in. 

= 3 sq. ft. 

_yr. = 1 yr. 6 mo. 

13 . 

mo. = 

= If yr. 

J A. = sq. rd. 

14 . 

9 sq. yd. = 

sq. ft. 

3j doz. = articles 

15 . 

.25 mi. = 

ft. 

. % of 1 gal. = 1 qt. 

16 . 

1 sq. yd. = 

sq. ft. 

.5 X 12 in. = in. 

17 . 

j gross = 


min. = 10 sec. 

18 . 

9 mo. =_ 

yr. 

8 yd. 18 in. =_yd. 

19. 

ft. = 

6 ft. 8 in. 

25 nickels = cents 

20 . 

9 ft. 3 in. = 

ft. 

f sq. yd. = sq. ft. 

21 . 

8 gal. = 

pt. 

lb. = 8 cwt. 

22 . 

nickels = $.75 

. 37 J X 1 mi. = ft. 

23 . 

1 sq. mi. = 

A. 

ton = 5500 lb. 

24 . 

1 hr. 15 min. = min. 

3 score and 10 = 

25 . 

.75 X 1 ft. 

= in. 

“ 8 lb. 10 oz. = _oz. 















































SEVENTH GRADE 


171 


126. Recording Your Progress in Arithmetic 

You are to keep a record of your progress in arithmetic 
this term on a line graph. 

On the next few pages in this book you will find tests 
which are marked Test I, II, III, IV, V, VI, VII, VIII, 
IX, X. There are 16 examples in each test. Try a new 
test every few weeks. 

Each time a test is given, record on the graph the 
number you have right. On a larger grapli your teacher 
will show the record of the class. Then you can compare 
your record with the class record. 

At the end of the term your record should be higher 
than at the beginning of the term. 

Things to Remember 

If you wish to improve your score, 

1 . Read your examples carefully. 

2. Think before you write. 

3. Check your work. 

4. Correct all mistakes and do some extra work on 
similar examples. 


172 THE BAYNE-SYLVESTER ARITHMETIC 


127. Tests 

You should complete each of these tests in about 30 
minutes. Work quickly but carefully. Accuracy is more 
important than speed. Check your answers. 

Test I 


1 . 7)49063 

2 . .4 + .3 + ’.2 = 

3. 7i - 6f = 

4. 30)1710 

5 . What is the quotient 
when 4 is divided by 

16 9 
2 1 • 

6 . f X 9 = 

7 . Find the product of 
86.24 and 9. 

8 . 647 
829 
368 
497 
678 
456 


9 . From 375 thousandths 
take 269 thousandths. 

10 . 25 is ? per cent of 125 

11 . 12i% of ? = 28 

12 . 6% of 2645 = 

13. Reduce to lowest terms: 

7 5 
T2~5 

14. 7.5 mi. = ? feet 

15. Find the perimeter of a 
rectangular plot that 
measures 3.5 rd. by 
4.5 rd. 

16. Four-fifteenths plus 
three-fifteenths plus 
two-fifteenths = 




SEVENTH GRADE 


173 


Test II 

11 . Find the product of .62 
and 4935. 


1 . ? = 4% of $25,500 

2 . Subtract: 



3. Three-fourths of twenty 
thousand = 

A 5 _i_ 5 _ 

6 . 73)5088.5 

6 . 56,740 ^ 28 = 

7. 200 is ? % of 400 

8 . Change 26 f to an im¬ 
proper fraction. 

9. .3 -h .5 -f .8 = 

10 . From 1.9 take 1.275. 


12 . Find the interest on 
$2600 at 5% for 1 year. 

IQ 3 4_ i — 

J-O. 4 -r 2 ^ 12 ■” 

14. 75% of ? = 630 

15. What is the area of a 
plot that measures 16 
rd. by 8i rd.? 

16. 7,846 

629 

3 

964 

47,829 

68,695, 

5,478 


tO|M 




174 


THE BAYNE-SYLVESTER ARITHMETIC 


Test III 


1. 94,864 

7,293 

66,280 

9,496 

75 

8 

8,245 

2. .15 + .26 + .17 = 

3. Multiply 8695 by 7.8. 

4. 1000 X 6.2467 = 

6. Five-sixths plus one- 
third = 

6. 2J minus f = 

7. What is the quotient 
when J is divided by 


8. Interest rate, 4%; time, 
1 year; principal, $1275. 
What is the interest? 

9. How many square feet 
are there in 4.5 sq. yd.? 

10. Reduce to a mixed 
number: 

11. 12 X 2f = 

12. Divisor 274 

Dividend 39,865 
Quotient ? 

13. 50 is ? per cent of 250 

14. 87i% of ? = 2163 

16. Find 37|% of $12.40. 

16. How much fence wire 
is needed to inclose a 
field 12.5 yd. square? 



SEVENTH GRADE 


175 


Test IV 


1. Find the difference be¬ 
tween 5 and .475. 

2. Multiply twenty-five 
hundredths by eighty- 
four. 

3. 200)64.26 

4. Dividend 456.1 

Divisor 3.5 

Quotient ? 

6. What is 60% of S5640? 

6 . .6 - .005 = 

7. .38 +.26 +.14 + .13 = 

8. What part of a square 
foot is 72 sq. in.? 

5 

rs- 

1 
3 
5 
8 


10 . 12 ^ 

- 9 ^ 

11. Three-eighths times 
four-ninths = 

12. 7^ 9 = 

13. 8 is ? % of 100 

14. S5 is 5% of ? 

15. 8624 
9378 
4695 
8769 
5684 
3698 

16. Find the area of the 
right triangle that has a 
base of 32 ft. and a 
height of 24 ft. 


9. 




176 


THE BAYNE-SYLVESTER ARITHMETIC 


Test V 

9. 8f 

26| 

30f 

7 


1 . Principal $1650 
Rate 6% 

Time 1 yr. 

Interest ? 

2 . Find the area of a 
square each side of 
which measures 26.25 
yd. 

3. Find the difference be¬ 
tween 57.08 and 15.018. 

4. Multiply: 

59.35 

.86 

5. .02 + .04 + .03 = 

6 . li X 3f = 

7. One-fourth minus two- 
eighths = 

8 . Find the quotient when 
2 j is divided by 


10 . 86,457 
29,836 
64 
928 
6,945 
7 


11 . How^ many square 
yards are there in 24 
rd.? 

12. 83.78 X 4000 = 

13. 75)18.362 

14. What is 8^% of 3640? 

15. 560 is ? per cent of 640 

16. Find the number of 
which $1200 is 66f%. 





SEVENTH GRADE 


177 


Test VI 


1. 6000 X 2.64 = 


2. 25)244.5 

3. What is 200% of $1600? 

4. 19.3 - 16.25 = 

5. Find the product: 

63.68 

.006 

6. Divide one by two- 
thirds. 

7. 9| + 6J + 4i -I- 6i = 

8. What is the difference 
between 7y^ and f ? 

9. Principal $2480 

Rate 4% 

Time 2 yr. 

Interest ? 


10. Subtract: 

7 hr. 5 min. 

6 hr. 15 min . 

11. f X 2i = 

12. Multiply: 

6462 

48f 

13. Find 125% of $18,000. 

14. 12% of ? = 2400 

15. 64,568 
29,364 

8,269 

548 

9,678 

49,006 

16. Find the distance 
around a rectangular 
plot that measures 8 ft. 
6 in. by 6 ft. 4 in. 







178 


THE BAYNE-SYLVESTER ARITHMETIC 


1. 13 

16f 

17i 

28 ^ 

2. 8i X f = 

3. 20 12i = 

4. 6i - i = 

6. Multiply: 

63.08 

.025 


6. Subtract: 

182.5 

6.275 


7. 8 gal. 3 qt. 
4 gal. 2 qt. 
6 gal. 1 qt. 


Test VII 

8 . 167.2 + 8.245 + 16.45 
+ 128 + 6.04 = 

9. Multiply: 

1645| 

426 

10. $64 ^ 75 = 

11. Find 115% of 3640. 

12. 1200 is ? per cent of 
1200 

13. What is the interest on 
$1500 for 6 months at 
6%? 

14. 15% of ? = 450 

15. 6.3 ^ 9000 = 

16. Find the area of a tri¬ 
angle whose altitude is 
18f ft. and whose base 
is 20| ft. 







SEVENTH GRADE 


179 


Test Vm 


1 . Find the product of 
4562.4 and 2600. 

2 . Subtract: 

16 ft. 9 in. 

7 ft. 11 in. 

3. Time 9 months 

Rate 3% 

Principal $12,000 
Interest ? 

4. 16 

28f 

7i 

29A 

5. From 29J take 131. 

6. 4i X 2f = 

7. 9.287 4- .38 = 


8 . Multiply: 

4600 

2641 


9. $800 is ? per cent of 
$400 

10 . 600 = 200% of what 
number? 

11 . = 

12 . Find the difference be¬ 
tween 20 and 3.75. 

13. .0125 X .54 = 

14. 463.5 + 4 4- 82.875 + 
600 + 60.06 = 

15. 63 2700 = 

16. Find the area of a tri¬ 
angle whose altitude is 
12.2 yd. and whose base 
is 36.6 yd. 





180 


THE BAYNE-SYLVESTER ARITHMETIC 


Test IX 


1 . Find the interest on 
$2600 for 1 year 8 
months at 4%. 

2. Add: 

8 lb. 6 oz. 

4 lb. 3 oz. 

9 lb. 8 oz. 

3. 8.2)8340 

4. Find .5% of $1600. 

5. 600 is ? per cent of 400 

6. 125% of ? = 400 

7. 4.62 ^ 4200 = 

8. 38i + f + 26 + 25i = 

9. Minuend 204| 
Subtrahend lOOj 
Remainder ? 


10. 4 X f X 6i = 

11- A ^ = 

12 . 86,423 
49,587 
69,286 
78,237 
45,968 
26,984 


13. From .375 take .25. 

14. A X 6.58 = 

15. 19.85 + 6.425 + 8.2 -f 
93 = 

16. Find the area of a tri¬ 
angle whose base is 6.75 
yd. and whose height is 
4.25 yd. 





SEVENTH GRADE 


181 


Test X 


1. .834 -r- 6000 = 

2 . Find of $1800. 

3. 1000 is ? per cent of 800 

4. Subtract .75 from 1.875. 

5. Find the product of 
62.46 and 32.45. 

6 . .26 + 1.246 + 375 + 
.4268 = 

7. 206i 

99f 

18 

6 # 


11 . Subtract: 

27 yd. 1 ft. 

18 yd. 2 ft . 

12 . 3f ^ l3^ = 

13. Divide 45.8 by .648. 

14. 75% of ? = 2700 

15. 86,954 
23,706 
85,499 
20,060 
67,868 
49,365 


8 . 84| minus f = 

9. 8i X 6f X 3i = 

10 . Rate 5% 

Principal $13,000 
Time 2 yr. 6 mo. 

Interest ? 


16. Find the area of a 
rectangular plot that 
measures 14.8 ft. by 
7.25 ft. 





SEVENTH GRADE —PART III 


128. Problems 

Without pencil. 

1. What will 10 qt. of milk cost at $.16 a quart? 

2. At $12.50 per ton, what must be paid (a) for 2 T. of 

coal? (h) For 6 T.? (c) For 10 T.? 

3. How much change should you receive from a two- 
dollar bill if your purchases amount to $1.65? 

4. Grapefruit are sold at the rate of 2 for 25^. Six 

grapefruit, at this rate, will cost_ 

5. Four dozen eggs at $.55 per dozen will cost- 

6. You give the clerk 3 one-dollar bills in payment for 
the eggs. He gives you $.80 in change. Is that correct? 

7. At $.80 per pound, how much candy can be bought 
(a) for $.40? (6) For $.60? (c) For $.20? (d) For $2.50? 

8. Bananas are sold at 45c^ per dozen or 4^ each. How 
much is saved by purchasing by the dozen? 

9. Corn sells at 22^ per can or $1.25 per half-dozen 

cans. I save_in purchasing by the half-dozen. 

10. At $.22 each, how many boxes of berries can be 

bought (a) for $f? (h) For $1^? 

11. Find the cost of 2| lb. of butter at 52^ per pound. 

12. Lemons which cost the dealer 40j^ per dozen are 

sold at the rate of 6 for 25^. (a) How much money does 

the dealer gain on a dozen? (6) What is the per cent of 
profit? 

13. Find the cost of 7 lb. of sugar at the rate of 3| lb. 
for 27^ and | lb. of coffee at 48^ per pound. 

14. What will 4 handkerchiefs cost (a) at 15each? 
(5) At $1.20 per dozen? 


182 


SEVENTH GRADE 


183 


15. What must I pay for 3 cakes of soap (a) at 8^ each? 
(6) At 80^ per dozen? (c) At 6 for 50^? 

16. Mary is baking a cake. Her recipe calls for f of a 
cup of milk, (a) How much milk should she use if she 
bakes a cake half the size of the one the recipe will make? 
(b) If she doubles the original recipe, Mary will need 
_cups of milk. 

17. If meat loses 25% of its weight in cooking, what 
will a 24-pound roast weigh after cooking? 

With pencil. 

18. The sales for one week in the Neighborhood Depart¬ 
ment Store were as follows: millinery, $475.83; boys’ 
clothing, $495.60; shoes, $395.72; men’s furnishings, 
$327.55; dry goods, $1757.29; notions, $187.79. Find 
the total amount of sales for the week. 

19. Mrs. White made the following purchases at the 
store on Tuesday: shoes, $7.50; umbrella, $3j; gloves, 
$lf; hat, $7.65. How much did she spend in all? 

20. State the amount of change a customer should 
receive from a $50 bill given in payment for the following 
purchases: 

3 pr. gloves at $1.85 3 yd. silk at $2.65 

2 pr. shoes at $7.75 24J yd. muslin at $.38 

21. Mrs. Brown spent $24f for silk at $2f per yard. 

She bought-yards. 

22. There were three extra clerks on duty at the dress- 

goods counter during the sale. On one day, the first 
clerk’s sales totaled $121.75; those of the second clerk, 
$97.55; those of the third clerk, $110.03. The total 
amount of sales for the day by the three clerks was- 


184 THE BAYNE-SYLVESTER ARITHMETIC 

23. In four consecutive weeks Mary Black, a clerk in 
the store, earned the following amounts: $22.70, $27.50, 
$30.50, and $25.75. What were her average weekly 
earnings? 

24. Mr. Jones made the following bank deposits last 

week: $1755.83; $1692.02; $1972.50; $1263.45; $1205.03; 
$1922.06. In all, he deposited- 

25. Joe Blake made the following deposits to his bank 
account in the last three months: $10f, $13J, and $20f. 
How much more must he deposit to make $75? 

26. Mr. Curry owns two adjoining farms. One farm 
contains 73.25 A.; the other contains 87.5 A. He sold 
27.7 A. of the second farm to Mr. Bond, (a) How many 
acres did Mr. Bond buy? (6) How many acres remain 
in the second farm? (c) How many acres does Mr. Blake 
still own? 

27. A train traveling at the rate of 37.9 mi. per hour 

covers_miles in 8 hr. 

28. 42.00 ^ 35 = ? 

26.25 35 = ? 

437.25 ^ 35 = ? 

12.25 35 = ? 

2625.00 35 = ? 

? 35 = ? 

29. It takes 2.5 yd. of ribbon to make a rosette, 
(a) How many yards must Mary buy to make a dozen 
rosettes? (5) How many rosettes can Mary make from 
a bolt of ribbon containing 10 yd.? (c) What will be the 
cost of each rosette if the ribbon costs $.38 per yard? 

30. A farm consisted of 40| A. of woodland and 54| A. 
of meadow land. The owner bought 63f A. additional. 
What was the total acreage of the farm then? 





SEVENTH GRADE 


185 


31. How much money is spent in equipping a kitchen 
as follows: 

Furniture Woodenware 

1 Gas Stove at $75.00, discount 10% 1 Towel Rack at $.75 
1 Small Table at $7.75, discount 5% 1 Rolling Pin at $.48 

1 Cabinet at $29.50, discount 5% 2 Brooms at $.85 each 

2 Chairs at $2.75 each, discount 5% 3 Brushes at $.79 each 

Earthenware Tinware 

1 Nest of Bowls at $1.78 1 Flour Sifter at $.40 

2 Pitchers at $.57 each 1 Bread Box at $1.25 

1 Cake Box at $.95 

32. Find the total cost of the furnishings listed below. 
A 10% discount is allowed on the furniture and rugs. 
A 15% discount is allowed on the electric washer. 


Living Room Dining Room 


Rug 

$75.00 

China Cabinet 

$75.85 

Table 

$62.50 

Table 

$87.50 

Bookcase 

$37.75 

4 Chairs at 

$ 7.95 each 

Desk 

$37.50 

Rug 

$58.50 

2 Chairs at 

$ 9.50 each 

Tea Wagon 

$21.60 

Bedroom 

Laundry 

Bed and Spring 

$50.75 

Electric Washer $195.00 

Dresser 

$47.50 



Chair 

$ 9.75 

Kitchen 

Table 

$ 7.85 

Stove 

$75.75 

Rug 

$14.75 

Cabinet 

$38.90 



Table 

$ 8.75 



2 Chairs at 

$ 3.85 each 


188 


THE BAYNE-SYLVESTER ARITHMETIC 


129. Practicing Thrift 

We have learned that thrift, or the wise management 
of money, leads to prosperity. Thrift, as a habit, leads to 
success in life. 

There are several ways of saving money. Perhaps the 
best way is to set aside a definite sum each week or month, 
and to deposit this sum regularly in a savings bank where 
it will earn interest. It is a good plan, too, to have a 
purpose in view when we save. A boy, for example, may 
save toward his college expenses; a girl may save in order 
that she may help to pay for a course in music. In these 
days, many banks have special Christmas Club accounts. 
By means of a Christmas Club account it is possible to 
save either a large or a small amount, depending on the 
size of the weekly deposit. In some banks one may join 
a Vacation Club. 

One may save money by taking advantage of the sales 
offered from time to time by the various stores. At such 
sales one may often buy needed articles at greatly reduced 
prices. 

Again, one may often save money by the prompt pay¬ 
ment of certain bills whenever a sum is deducted from the 
amount of the bill if paid within a certain time. Good 
business men always take advantage of this means of 
saving money. 

But true thrift does not consist merely in the wise use 
of money. One may be thrifty in other respects. Care¬ 
ful use of our time, proper care of our clothing and other 
personal belongings, and proper treatment of our school¬ 
books and other public property are all true forms of 
thrift. 


SEVENTH GRADE 


187 


130. Discount Sales 

Early in January, Mr. Gray advertised a sale of furni¬ 
ture at a reduction of 20% below the regular cost. Mrs. 
Ames bought a sofa which had been marked $75.60. 
How much did she save by buying at the reduced price? 


1 $15.12, 

20% = i |X = $15.12 saved 


In business the regular price of an article is called the 
list price. W^hat was the list price of the sofa bought by 
Mrs. Ames? \Mien an article is sold at less than the list 
price, it is sold at a discount. The discount, in such 
cases, is the amount deducted from the regular or list 
price. When the discount is expressed as a certain per 
cent, we speak of it as the rate of discount. What is the 
rate of discount in the example above? What is the 
discount? 

Discount, you will note, is another of the business 
applications of percentage. 

Finding the discount is the same as finding a_of a 

number. 

1. Tell at sight the amount of discount on each of the 
following if the rate of discount is 20% off list prices: 


Article 

List Price 

Article 

List Price 

(a) Vanity Lamps 

$3.50 

(d) French Pottery 


(6) Bridge Lamps 

$4.00 

Lamps 

$15.00 

(c) Italian Pottery 


(e) Bronze Reading 


Lamps 

$7.50 

Lamps 

$10.50 

(/) Metal Table Lamps $25.00 





188 


THE BAYNE-SYLVESTER ARITHMETIC 


2. Find the amount saved on each article by purchasing 
it at the sale: 


Article 

List Price 

Rate of Discount 

(a) Sewing Tables 

$18.00 

20% 

(5) Chairs 

$15.00 

20% 

(c) Mirrors 

$27.50 

15% 

{d) Buffets 

$49.50 

10% 

(e) Dining Tables 

$75.75 

20% 

(/) Beds 

$36.00 

25% 


131. Finding the Net Cost 

At a special sale of overcoats, Mr. James bought a coat 
regularly marked $65 at 20% off. (a) What was the dis¬ 
count? (b) How much did Mr. James pay for the coat? 


, 20% = i 

I X $65 = $13, discount 
$65 — $13 = $52, sum paid for the coat 
$52 = net cost of the coat 


The net cost of an article is the regular cost minus the 
discount. 

Explain how the net cost was found in the example 
above. 

1. A radio set listed at $250 was sold at a 30% dis¬ 
count. For what price was it sold? 

2. At 2|% discount for cash, find the sum paid to 
Mr. Grant in settlement of each of the following bills: 

(a) $175.50 (d) $148.00 

(h) $300.00 (e) $275.00 

(c) $1200.00 (/) $328.00 



SEVENTH GRADE 


189 


3. Complete the following: 


Article 


Rate of 

List Price Discount Discount Net Cost 


(a) Grass Shears 
(5) Garden Shears 


$2.00 15% 

$3.50 20% 

$1.75* 20% 

$2.25 20% 

$1.50 30% 


(c) Spade 
{d) Hoe 
(e) Rake 


(/) Lawn Mower $35.00 30% 

{g) Lawn Mower Jr. $27.50 20% 

{h) Lawn Sprinkler $7.50 30% 

4. Many publishers allow a discount of 20% to stu¬ 

dents. What must a student pay for a book listed (a) 
at $3.75? (6) At $1.80? (c) At $1.25? (d) At $2.50? 

5. What is the net amount of a bill of goods the list 
price of which is $90.60 with 5% off for cash? 

6. What were the cash prices paid for the following at 
a sale of used cars at which a discount of 20% was given 
on all cars: (a) Ford, $420; (5) Dodge, $640; (c) Buick, 
$825; (d) Cadillac, $975; {e) Studebaker, $850? 

*7. A dealer sells $1500 worth of goods at 5% discount 
if the bill is paid within 60 days, or 10% discount if the 
bill is paid at once. What amount would be saved by 
prompt payment? 

8. A bargain sale of dress goods is advertised, at 
which a 33^% discount is offered, (a) What would be 
saved by purchasing at bargain prices 12 yd. of velvet, 
listed at $2.70 per yard, and 10 yd. of silk, listed at $1.80 per 
yard? (5) What would be the net cost per yard of the 
velvet? (c) Of the silk? 


190 THE BAYNE-SYLVESTER ARITHMETIC 

9. What will be saved by purchasing the following 
articles at a bargain sale which advertises a reduction of 
25%: 6 books listed at $1.60 each, and 3 fountain pens 
listed at $2.88 each? 

10. Goods amounting to $675 were purchased on 
June 1. Terms: 3 months, or 10% off for cash. What 
can be saved by paying the bill on June 1? 

*11. One store lists a book for $3.50 cash. Another 
store lists the same book for $4.25 with a discount of 25%. 
Which is the lower price, and how much lower is it? 

12. Find the net cost of 2 doz. pens, listed at $2.50 
each, if a discount of 16f% is allowed. 


132. Trade or Commercial Discount — 
Successive Discounts 

You have learned that goods are often sold for less than 
the marked or list price. Goods sold in this way are said 

to be sold at a_Discounts are allowed for several 

reasons: (1) for the prompt payment of bills; (2) on 
quantity purchases; (3) at special discount sales, when 
the dealer wishes to make a quick “turnover” of his stock. 

In many lines of business, merchants sell both at whole¬ 
sale and at retail. In their catalogues, goods are adver¬ 
tised at certain prices. Dealers are allowed a trade dis¬ 
count on these prices. 

Mr. Brown deals in furniture. He buys stock listed at 
$7500 from the Crown Manufacturing Company and is 
allowed a trade discount of ,30%, with an additional 5% 
off for cash. He pays his bill at once. What does the 
furniture cost him? 


SEVENTH GRADE 


191 


What rate of discount was Mr. Brown allowed on his 
bill? What did this discount amount to? What was the 
net cost of the furniture minus the trade discount? 

Dealers are often allowed two or even three successive 
discounts on the same purchase. In addition to the 30% 
trade discount, Mr. Brown was allowed a 5% discount for 
cash. What did the cash discount amount to? What 
was the net cost of the furniture? 


$7500 list price 

$7500 

$5250 

$5250 

.30 

$2250 

.05 

$262.50 

$2250.00 

$5250 

$262.50 

$4987.50 

trade discount 

list price 

cash discount 

net cost 

minus 

3 trade discount 




In computing discount when two discounts are allowed, 
the second discount is always computed on the sum left 
after the first discount has been deducted from the list 
price. The sum left after both discounts have been de¬ 
ducted is the _ of the bill. The net price, then, is 

what is actually paid for an article after all discounts have 
been deducted. 

1. Find the net price of the following: 

(а) 6 chairs at $9.50 each, with discounts of 20% 

and 5%. 

(б) 2 tables at $75.00 each, with discounts of 25% 

and 5%. 

2. Mr. Allen buys $1500 worth of dry goods and 
receives discounts of 15% and 10%. What is the net 
cost of the goods? 








192 THE BAYNE-SYLVESTER ARITHMETIC 

3. The discounts on a piece of machinery listed at 
$2560 are 25% and 10%. What is the net price? 

4. If the order of the discounts was reversed in Prob¬ 
lem 3, what would the net cost be? 

5. Which is better for a purchaser: a single discount 
of 25% or successive discounts of 15% and 10% on a bill of 
$720? 

6. A piano listed at $900 was sold with discounts of 
15% and 10%. Find the net cost. 

7. Find the net cost of goods listed and discounted as 
follows: 

(a) $300 30% and 20% (d) $750 15% and 10% 

(b) $200 25% and 5% (e) $750 10% and 15% 

(c) $420 25% and 12j% (/) $900 20% and 10% 

8. An automobile tire is listed at $25. One dealer 
offers discounts of 10% and 10%. A second dealer offers 
a single discount of 20%. Which is the lower price? 

9. Find the net cost of each of the following: 

(a) 12 tires at $12.50 each, discounts 15% and 5%. 

(b) 18 yd. of velvet at $4.50, and 12 yd. of satin 

at $2.25, discounts 20% and 20%. 

10. A check for_will settle a bill of goods amount¬ 

ing to $825, with discounts of 10% and 5%. 

11. A grocer received a bill for 60 bbl. flour at $6.25 
per barrel. He is allowed a trade discount of 15% with 
5% for cash. What does the flour cost him if he pays for 
it promptly? 

*12. Mr. Francis receives a bill for $528 marked: 
Terms: 2/10; n/30.” The trade discount allowed is 
12^%. What is the net cost to Mr. Francis if the bill is 


SEVENTH GRADE 


193 


paid at once? (Note: 2/10 means ^^2% if paid within 
10 days.” n/30 means that the bill must be paid within 
30 days. Will the cash discount be allowed if the bill 
runs 30 days? How do you know?) 

Complete these statements: 

1. The regular price of an article is called the_price. 

2. When an article is sold at less than the list price, 

it is said to be sold at a_ 

3. The amount deducted from the regular or list price 

is called the_ 

4. The net price of an article is its cost after the_ 

has been deducted from the_ 

5. How do you find the net cost of an article on which a 
discount has been allowed? 

133. Interest—^ Review 

Complete the following sentences: 

1. Money paid for the use of money is called- 

2. The sum of money on which interest is paid is called 

the_ 

3. The per cent of the principal paid each year as 

interest is called the_ 

4. The period for which interest is paid is called the 


5. The sum of the principal and interest is called 

the _ 

6. The interest which a borrower has to pay depends 

upon the _ , the _ of interest, and the _ for 

which the money is borrowed. 

Interest is one of the business applications of percentage. 















194 


THE BAYNE-SYLVESTER ARITHMETIC 


What is the interest on $400 at 6% for 1 year 6 months? 



To find the interest, multiply the principal by the 
rate expressed as a fraction and by the time expressed 
as a fraction of a year. 


Following this rule, find the interest on each of the fol- 


lowing: 

Principal 

Rate 

Time 

Principal 

Rate 

Time 

1. $200 

6% 

1 yr. 6 mo. 

8. $750 

4% 

i year 

2. $400 

4% 

years 

9. $250 

5% 

3 yr. 8 mo. 

3. $600 

6% 

Ij years 

10. $1200 

6% 

9 months 

4. $700 

6% 

1 year 

11. $2000 

4% 

6 months 

5. $900 

6% 

1 year 

12. $1500 

6% 

9 months 

6. $450 

6% 

2 years 

13. $3000 

6% 

1 yr. 6 mo. 

7. $750 

5% 

3 years 

14. $5500 

6% 

2 yr. 3 mo. 


134. Interest for 30, 60, 90 Days — the 6% Method 

In order to buy new stock for the holiday trade, Mr. 
Elliott needed $5000 in cash. He borrowed the money 
for 60 days at 6% interest. How much interest did he 
have to pay? 

Money is often borrowed for short periods of time — for 
example, for 30, 60, or 90 days. In computing interest 




SEVENTH GRADE 


195 


for such periods, it is customary to reckon 360 days to the 
year. Then each day’s interest equals 3 ^ of a year’s 
interest. 

At 6 %, the interest on any sum for 1 year equals .06 of 
the principal. At 6 %, the interest for 60 days, or | of a 
year, equals .01 of the principal. (Interest for 60 days 
= 4 of 6 % = 1 % = . 01 ) 

Therefore, to find the interest on any sum for 60 days 
at 6 %, we find .01 of the principal. 

In Mr. Elliott’s case: interest on $5000 for 60 days = 
.01 of $5000, or $50. 


To find the interest on any sum for 60 days at 6%, 
move the decimal point in the principal two places to 
the left. 


1 . What is the interest on each of the following sums 
for 60 days at 6 %? 

(a) $750 (c) $705 (e) $4000 {g) $85 (i) $965 

(5) $9570 (d) $1875 (/) $352 (h) $175 (j) $1450 

If you knew the interest on a certain sum of money for 
60 days at 6 %, how would you find the interest for 30 
days? 

What is the interest on $300 for 30 days at 6 %? 


Interest on $300 for 60 days = $3.00 

Interest on $300 for 30 days = J of $3.00 = $1.50 


2 . Tell at sight the interest on each of the following 
sums for 30 days at 6 %: 




196 THE BAYNE-SYLVESTER ARITHMETIC 

(а) 11000 (c) 1700 (e) 1250 {g) 1760 (t) 1570 

( б ) S1200 (d) 1900 (/) $2400 {h) $3000 (j) $220 

3 . Complete the following: 

(a) To find the interest for 60 days at 6 %, take-% 

of the principal. 

(b) To find the interest for 30 days at 6 %, take-of 

the interest for 60 days. 

Suppose that Mr. Elliott had borrowed the $5000 tor 
90 days. How much interest would he have had to pay 
at the end of the 90 days? 

90 days = 60 days +- 

The interest on $5000 for 60 days at 6 % = $50.00 

The interest on $5000 for 30 days at 6 % = - 

The interest on $5000 for 90 days at 6 % = - 

For 90 days, Mr. Elliott would pay-interest on the 

$5000 he borrowed. 

4 . Tell at sight the interest on each of the following 
sums for 90 days at 6 %: 

(a) $450 (c) $800 (e) $4200 {g) $2700 (f) $2100 

(b) $380 (d) $1500 (/) $760 (b) $1800 (i) $3800 

6 . Find the interest on $4000 at 6 % (a) for 60 days; 
(b) for 30 days; (c) for 90 days. 

6 . Find the interest on $360 at 6 % (a) for 60 days; 
(b) for 30 days; (c) for 90 days. 

7 . What is the interest at 6 % on $470 (a) for 60 days? 
(b) For 30 days? (c) For 90 days? 

8 . What is the interest at 6 % on $7000 (o) for 60 days? 
(b) For 30 days? (c) For 90 days? 







SEVENTH GRADE 


197 


Let us suppose that Mr. Elliott was able to borrow the 
$5000 he needed at 4% interest instead of at 6%. How 
would that fact affect the amount of interest to be paid? 


4 = f of 6 

,At 6%, the interest for 60 days on $5000 = $50 
At 4%, the interest for 60 days on $5000 = f X $50 
f X $50 = = $33.33J interest at 4% 


What is the interest on $300 for 60 days at 4%? 


Interest on $300 for 60 days at 6% = $3.00 

2 $ 1.00 

Interest on 300 for 60 days at 4% ^ ^ $Jj0O^= $2.U0 


To find the interest on any amount at 4%, first find 
the interest at 6%. Then take f of this amount for 
the interest at 4%. 


Use pencil if needed. 

Find the interest at 4% on each of the following sums for 
the time given: 


1. $200, 60 days 

2. $900, 60 days 

3. $1200, 30 days 

4. $1500, 90 days 

5. $750, 60 days 


6. $400, 60 days 

7. $700, 60 days 

8. $1400, 90 days 

9. $1800, 30 days 

10. $1250, 90 days 







198 THE BAYNE-SYLVESTER ARITHMETIC 

11. Complete the following statements: 

(a) The interest on any sum for 60 days at 6% is- 

of the princ pal. 

(h) When 360 days are reckoned as a year, the interest 
for 60 days at 6% is \ of the interest for a year. 

(c) To find the interest on any sum for 30 days at 6%, 
take_of the interest for 60 days. 

Without pencil. 

12. Tell at sight the interest on each of the following 
sums for 60 days at 6%: 

(а) $1200 (d) S1550 {g) $4225 O') $165 

(б) $875 0) S1600 (h) $427 (/c) $1650 

(c) $950 (/) $1775 (i) $9660 il) $65 

13. Compute the interest on each of the following 
sums for 30 days at 6%: 

(a) $1260 (d) $250 {g) $387 0) S1475 

(5) $960 0) S4400 Qi) $3870 {k) $478 

(c) $1220 (/) $440 0) $75 il) $3779 

14. What is the interest on each of the following sums 
for 90 days at 6%? 

(a) $328 (d) $1250 {g) $4500 0) S1468 

(5) $7425 0) S745 {h) $4020 {k) $468 

(c) $875 (/) $8000 (i) $380 (0 $7550 

15. Find the interest at 4% on each of the following 
sums, first for 60 days; then for 30 days; then for 90 
days: 

(a) $1200 (d) $4000 {g) $8000 O') $2700 

(5) $750 (e) $4500 [h) $8020 (k) $6850 

(c) $1500 (/) $4250 {%) $8575 {1) $4780 





SEVENTH GRADE 


199 


135. General Problems in Interest 

With pencil. 

1 . On March 1 a merchant borrowed $3000 from a 
bank, arranging to repay the loan with interest at 6% on 
June 1. He paid the bank $3045. Was that the correct 
amount? How much of this sum was interest? 

2. A man borrowed $12,000 to invest in a fruit farm. 
What is the yearly interest at the rate of 6%? 

3. A town borrows $150,000 at 5% for the purpose of 
improving its highways. Find the yearly interest on this 
loan. 

*4. A man borrowed $500 on November 1 and repaid 
the loan on May 1 of the following year with interest at 
6%. He needed_to cancel the debt. 

5. How much interest is due on a loan of $1850 for 
6 months at 4%? 

*6. Estimate the interest on $700 for Ij years at 6%. 
Then work the example and compare your answer with 
the estimated answer. 

7. A man borrowed $1500 for years at 5% interest, 
(a) How much interest did he pay yearly? (5) How 
much interest did he pay in the 2j years? 

*8. The interest on $16,000 at 6% would pay the rent 
of a house at the rate of_a year or_a month. 

9. Mr. Flood borrowed $2700 for 2^ years, paying 
interest at the rate of 6%. At the end of each year he 
paid the interest then due. (a) What was the amount 
he owed at the final settlement of the debt? (6) If he 
had paid no interest until the end of the 2| years, what 
amount of money would he have needed to settle the 
debt? 





200 


THE BAYNE-SYLVESTER ARITHMETIC 


136. The Interest Formula 


To find interest on any sum, multiply the principal 
by the rate expressed as a fraction and by the time 
expressed as years or a part of a year. 


Interest = principal X rate X time, or i — prt 
Mr. Green borrowed $120 for 2| years at 4%. How 
much interest did he pay in all? 


i = pH 

$ 1 . 20 , \ 5 

i = $>^X 2 = 


Work the following examples in the same way. First 
give the value of p, r, and t in each. Then find the interest: 

1. $500 for 2| years at 4% 3. $350 for 1^ years at 6% 

2. $200 for li years at 5% 4. $780 for 2^ years at 4% 

The amount = principal plus interest. Then 

a = p i 


I borrowed $200 for 2 years at 4%. (a) What was the 

total interest? (5) What was the total amount repaid? 


I' 

II 

a = p + i 

i = ^20er1< ^ X 2 = $16 

a = $200 + $16 = $216 


6. Apply the formula a = p + f to Examples 1-4. 





SEVENTH GRADE 


201 


137. Compound Interest 

Ned worked during one summer vacation and earned 
$200 which he put into a savings bank to save for his college 
education. The bank manager told him that if he allowed 
it to stay in the bank, they would pay him 4% compound 
interest, and that the interest would be compounded 
quarterly. This was not the same kind of interest as 
simple interest. Compound interest meant interest not 
only on the principal but also on the interest already due. 
It worked out in this way: 


1200 principal; 4% rate at compound interest, compounded quarterly 

4% a year = 

1 % every 3 months, or each quarter year 

$200 Principal for first quarter 

.01 

$2.00 

Interest for quarter year 

200 

Principal for first quarter 

$202 

Principal for second quarter 

.01 

$2.02 

Interest for second quarter 

202 

Principal for second quarter 

$204.02 

Principal for third quarter 

(Do not compute compound interest on sums less 

.01 

than $1.) 

$2.04 

Interest for third quarter 

204.02 

Principal for third quarter 

$206.06 

Principal for fourth quarter 

.01 

$2.06 

Interest for fourth quarter 

206.06 

Principal for fourth quarter ^ 

$208.12 

Ned’s account at end of first year 

Compound interest for 1 year = $8.12 


The simple interest on $200 for 1 year at 4% would be 
$8.00. You see that Ned would receive $.12 more by 










202 THE BAYNE-SYLVESTER ARITHMETIC 


getting compound interest than he would at simple 
interest. 

Note the following facts about compound interest: 

1. Compound interest amounts to more than simple 
interest at the same rate. 

2. Compound interest is interest not only on the 
principal but also on the interest already due. 

3. The computation of compound interest is a series of 
interest problems with a changing principal each period. 

Suppose the interest had been compounded semiannu¬ 
ally instead of quarterly. 


4% annually = 2% semiannually 
$200 Principal for first six months 
.02 

$4.00 Interest for first six months 
200 

$204 Principal for second six months 
.02 


$4.08 

204 

$208.08 Ned’s account at the end of 1 year 


Interest compounded semiannually will amount to less 
than interest at the same rate compounded quarterly. 


Calculate 

the compound interest: 


Principal 

^ Rate 

Time 

Compounded 

1. $300 

4 % 

2 years 

Semiannually 

2. $500 

4% 

1 year 

Quarterly 

3. $2000 

6% 

1 year 6 months 

Semiannually 

4. $250 

4% 

1 year 

Quarterly 

=5. $2500 

^% 

1 year 6 months 

Semiannually 







SEVENTH GRADE 


203 


138. Problems 

1 . A boy received a prize of $50 which he deposited 
in a savings bank which pays 4% interest compounded 
semiannually. What did this amount to in 2 years? 

2. What will $1000 amount to in 1 year if interest at 
4% is compounded quarterly? 

3. Allen transfers $20.50 from his school bank to the 
savings bank. How much will he have in a year if he 
receives 4% interest compounded quarterly? 

4. Find the difference between simple^ interest at 4% 
and compound interest at the same rate compounded 
quarterly for 1 year on $400. 

5. On October 1,1 deposited $500 in the Essex Savings 
Bank, which pays 4% interest compounded quarterly. 
On July 1 of the next year I withdrew all my money. 
How much did I withdraw? 

*6. Find the amount on $250 for 1 year 6 months at 
interest compounded semiannually. 

*7. (a) What will $425 amount to at compound interest 
at 4% in 4 years if the interest is compounded annually? 
(b) What will it amount to at simple interest at the same 
rate? 

*8. Which will earn more money and how much more 
will it earn: $3000 deposited in a bank for 1 year at 4%, 
compounded quarterly, or the same amount invested in a 
business yielding 5% annually? 

*9. At the end of 2 years I shall need $1350. If I 
deposit $1200 now in a bank paying 4% interest, com¬ 
pounded semiannually, and leave it there for 2 years, (a) 
shall I have enough? (6) If not, how much more shall I 
need? 


204 


THE BAYNE-SYLVESTER ARITHMETIC 


139. Banks 

William was a pupil in Grade 7A of a public school. 
For several years he had been putting money in the school 
bank. One day his father told him that they were going 
to move, and that since he would have to change schools, 
he had better withdraw his money from the school bank 
and deposit it in a savings hank. William withdrew the 
money and went with his father to a savings bank and 
deposited his savings. He now has an account of $20.50 
in a savings bank in his own name. The savings bank 
takes care of his money and pays him 4% a year interest 
or 1% every three months. 

At first William wondered how the bank could do this, 
for he thought, as many young people think, that the 
bank kept in its vaults the money he had deposited. His 
father explained that the savings bank lends the money 
which it receives to other persons to help them build 
houses or carry on business, and charges 5% or 6% interest 
on the loans. Because of the higher rate of interest which 
the bank receives from the persons to whom it lends 
money, it can pay William 4% interest on his deposit 
and still have money left over to pay the expenses of 
running the bank. William also learned that he cannot 
withdraw money from day to day without losing interest. 
The bank will not give him interest on money unless he 
leaves it there for at least three months or for the interest 
period. 

Business hanks or commercial hanks receive deposits, 
lend money on notes, and invest money in many more 
ways than do savings banks. They must always keep a 
certain part of their total deposits on hand. Money de- 


SEVENTH GRADE 


205 


posited in a business bank may always be withdrawn by 
the depositor by check. William’s father had his account 
in a business bank and could therefore pay his bills by 
check. William asked if he might go with his father the 
next time he went to his bank. His father agreed, and 
later they went to the bank. William’s father wished to 
deposit $150 in cash and a check for $220. First he made 
out a slip that looked like this: 


DEPOSITED TO THE ACCOUNT OF 

William Anderson 


IN 

THE SUFFOLK NATIONAL BANK 

ALL ITEMS ACCEPTED SUBJECT TO THE CONDITIONS STATED 

ON THE REVERSE SIDE OF THIS DEPOSIT SLIP. 

date 19^0 

PIT-T 

DOLLARS 

CENTS 

150 


SPECIE 



CHECKS 

220 






370 



























206 THE BAYNE-SYLVESTER ARITHMETIC 

Then he took the slip, his pass or deposit book, and 
what he was depositing to a window marked Receiving 
Teller.” The teller examined the slip and the deposits 
and entered in the pass book the full amount, $370. Mr. 
Anderson now had added $370 to his account at the bank. 

1. What difference do you note between a savings bank 
and a business bank? 

2. Which is better for saving money? 

3. Which is more convenient for paying bills? 

4. What is a deposit slip? 

5. Which kind of bank is most useful for boys and 
girls? 

6. Make out a deposit slip in your name for $100 in 
checks, $35 in bills, and $2.50 in silver. 

140. Paying Bills by Check 

William’s father called him in at the end of the week to 
show him how he made out checks for his bills. His first 
bill was for $70 owed to the Adirondack Lumber Company 
of Canton, New York. This is how the check looked; 


No. ^ New York, Jan. 10, 1930 

THE SUFFOLK NATIONAL BANK 
Pay to the Order of Adirondack Lumber Company % 70 yi^ 
Seventy - '—-- Dollars 


William Anderson 









SEVENTH GRADE 


207 


Then he filled out a small leaf left in his check book, 
called the stub, and explained to William that it is very 
important for any one who uses checks to fill out all the 
items accurately so that he may know how much his 
balance is and when he made out the check. 


No. bJll _$ 70.00 

Jan. 10 19 50 

Xo Adirondack Lumber Company 


Por box material 


Balance brought forward 

3285 

90 

Amount deposited 



Total 

3285 

90 

Amount this check 

70 


Balance carried forward 

3215 

90 


The bank keeps its own record, and every month Mr. 
Anderson receives from the bank all the checks that have 
come back, as well as a statement of his account showing 
his deposits, his withdrawals, and the balance left in his 
account. Mr. Anderson said he kept the returned checks 
carefully because he could use them at any time as receipts. 
This statement interested William. He asked: ''How 
can you prove that the right man received the check?’’ 
His father showed him a returned check on the back of 
which was the signature of the person to whom the check 
was made payable. "That signature on the back is called 



















208 


THE BAYNE-SYLVESTER ARITHMETIC 






























SEVENTH GRADE 


209 


the indorsement,” said his father, ^‘and that proves to 
me that he received the money.” The back of the check 
looked like this: 


Henry Watkins 


Before a check can be cashed or deposited in a bank, 
the person to whom it is payable must indorse it on the 
back. An indorsement is absolutely necessary. It should 
be written across the left end of the check. 

One thing more troubled William. How did the bank 
know that his father signed those checks? Mr. Anderson 
explained that before he opened his account at the bank 
he had to sign his name twice as specimens of his signature. 
His signatures on checks were compared with those on 
record at the bank to make sure that they were his. 

Read the check on page 208. To whom is it made 
payable? For what amount? Who wrote the check? 
On what bank is it drawn? On what date? Why is the 
check numbered? Why is the amount written in two 
ways? What must Mr. Grant do before he cashes or 
deposits the check? 

How does the bank know that Mr. Gorman made out 
this check? What does Mr. Gorman do with the check 
when it is returned to him? 

What use is made of the stub? Why does the stub 
state for what purpose the check was made? 

Write a check in payment of a bill from a gas com¬ 
pany. 





210 


THE BAYNE-SYLVESTER ARITHMETIC 


141. Keeping an Account at the Bank 


Mr. Gordon had an account at the Greenwich Bank. 
At the beginning of the week his balance amounted to 
$2406.50. During the week his deposits and withdrawals 
were as follows: 

Deposits Withdrawals 


Monday $16.50, $27.75, $18, $28.46, $32.68 

Tuesday $18.95, $27.63, $100.90 

Wednesday $43.65, $64.82, $90.75, $84.38 
Thursday $62.50, $8.25, $97.54, $125 

Friday $82.25, $75, $24.35, $86.24, $92.50 

Saturday $175, $248.40, $16.75, $13.50 


$25.75, $15, 
$1.75, $24.60 
$45, $26.50, $8 
$115.75 
$75, $52.25 
$125, $25.50 
$225, $15.75 


1. Find the balance at the end of each day. 

2. Find the balance at the end of the week. 

3. How much more had Mr. Gordon to his account at 
the end of the week than at the beginning? 


142. Finding Interest from a Graph 

It is possible to approximate interest by using the 
graph on page 211. From this graph you can find the 
interest for 1 year at 4% or 6% on principals to $1000. 
To find the interest for more than one year or for a part 
of a year, multiply the interest for one year by the 
appropriate whole number or fraction. 

For example, to find the interest on $200 at 4% for 
1 year, find $200, the principal, on the graph and run 
your finger up the vertical line until it crosses the 4% rate 
line. Then move your finger to the left along the hori¬ 
zontal line to the interest, which is $8. For 2 years the 
interest would be 2 X $8, or $16. For 6 months it would 
be J X $8, or $4. 


SEVENTH GRADE 


211 



TJse the graph in solving the following problems: 

1. Find the interest on 1600 for 1 year (o) at 6%; 
(b) at 4%. 

2. Find the interest on 1400 for 1 year (a) at 4%; 
(&) at 6%. 

3. What is the interest on $800 for 1 year (a) at 6%; 
(b) at4%? 

4. What is the interest on $500 for 1 year (a) at 6%; 
(6) at4%? 

6. Find the interest on $700 for 1 year (a) at 4%; 
(b) at 6%. 

6. Find the interest on $900 at 6% (a) for 1 year; 
(6) for 2 years. 

7. What is the interest on $1000 at 4% (a) for 1 year; 
(6) for 2 years; (c) for 3 years? 
























































































































212 


THE BAYNE-SYLVESTER ARITHMETIC 


8 . Find the interest on $300 at 4% (a) for 4 months; 
(h) for 8 months; (c) for 6 months. 

9. Find the interest on $600 at 6% (a) for 6 months; 
(h) for 3 months; (c) for 9 months. 

*10. Find the interest (a) on $1200 for 1 year at 6%; 
(b) on $2000 for 1 year at 4%; (c) on $1600 for 1 year at 
4%. 

11. Make up a problem to be solved from the graph. 

What principal will earn $24 in 1 year at 4%? 

To solve this problem, find $24 in the interest column; 
then move your finger to the right along the horizontal 
line until it crosses the 4% rate line; then follow down on 
the vertical line to the principal, which is $600. 

12. What principal will earn $30 in 1 year at 6%? 

13. What principal at 4% will earn $20 in 1 year? 

14. What principal at 4% will earn $30 in 1 year? 

15. What principal at 6% will earn $48 in 1 year? 

16. What principal at 4% will earn $28 in 1 year? 

17. Verify the answers in Problems 4, 8, and 12. 

*18. A business man borrowed a sum of money for 
6 months at 6%. If he had to pay $30 interest, what 
sum did he borrow? 

*19. Construct a similar graph that will show interest at 
2%, 3%, 5%, 7%, 8%. 

(Hint: Find the interest line for 2% on $1000. Draw 
the rate line from 0 to this point.) 

20. Make up problems similar to Problems 1-16 that 
can be solved from your graph. 


SEVENTH GRADE 


213 


143. Problems in Interest 

1 . What is the interest on $2250 for 1| years (a) at 

6%? (h) At 5%? 

2. Mr. Williams borrowed $4750 from his bank at 

6%. (a) How much interest must he pay every six 

months? (5) How much must he pay in interest if the 
loan runs for 2| years? 

3. A man borrows $1850 at 5%. How much interest 
is paid on the debt in 3 years? 

4. What is the interest on $690 at 4% for 2 years 
6 months? 

5. A senior in college borrows $250 from the Student 
Aid Fund to help him through the year. How much does 
he pay in interest at 4% if he keeps the money for 1 year 
6 months? 

6. Mr. Jones wishes to buy a lot which costs $3500. 
He has $3000 on hand. If he borrows the remainder from 
his bank for 60 days at 6%, what does the lot really cost 
him? 

7. Mr. Franklin has the following sums out at interest: 
$750 at 5%; $1280 at 4%; $1075 at 6%. How much 
does he receive in interest each half-year? 

8 . Find the interest on each of the following sums, at 
the rate given, and for the time indicated: 


Principal Rate Time Principal 

{a) 1500 4% 2 years (/) 1430 

(6) S720 5% 2 yr. 3 mo. {g) $1450 

(c) $650 6% 1 yr. 6 mo. {h) $385 

{d) $775 6% 2 yr. 10 mo. (t) $2470 

(e) $340 4% l yr. 3mo. O') *425 


Rate Time 

5% 1 yr. 9 mo. 
6% 60 days 
4% 30 days 
5% 2 yr. 8 mo. 
4% 90 days 


214 


THE BAYNE-SYLVESTER ARITHMETIC 


144. Compound Interest 

1. Find the compound interest on $400 for 2 years 
at 4%, payable half-yearly. 

2. (a) What is the simple interest on $620 for 2 years 

at 4%? (b) What is the compound interest on the same 

principal, for the same time, at the same rate, interest 
compounded semiannually? (c) What is the difference 
between the simple and the compound interest? 

3. When James Leslie was 12 years old, his father 
placed $250 to his account in the Newton Savings Bank 
at 4% compound interest. What will this sum amount to 
in 2 years, if the interest is compounded every six months? 

4. If $1250 is deposited at 4%, compounded semi¬ 
annually, what will it amount to in 2 years? 

5. Compute the compound interest on a deposit of 
$385 compounded semiannually for 1 year 6 months at 4%. 

6. Julia has $380 on deposit in a savings bank which 
pays interest at 4% payable half-yearly. If the account 
is left undisturbed for 2 years, how much will Julia have 
on deposit? 

*7. How would you find the compound interest on $800 
left to draw interest for 3 years at 4%, compounded semi¬ 
annually? 


145. Problems in Percentage 

1. A car averaged 16.4 mi. per gallon of gasoline before 
the carburetor was adjusted. After the adjustment it 
averaged 20.5 mi. What was the per cent of increase in 
mileage? 

2. Membership in the City Club increased from 400 
to 475. What was the per cent of increase? 


SEVENTH GRADE 


215 


3. During the school year the register of a school 
increased 400. This was 25% of the register on the first 
day in September. What was the register on the last 
day of June? 

4. An auditorium seats 550 pupils. If there are 2200 
pupils in the school, what per cent can be seated at a time? 

5. Mr. Dean bought an old house for $3600. He 
spent $1400 to repair and paint the house and then sold 
it at a profit of 15%. What was the selling price? 

6. A farmer with a herd of 180 cows sold 16f% of the 
herd at an average price of $115 each. What did he 
receive for the cows he sold? 

7. A grocer bought a case containing 240 oranges. 
He found that 24 were spoiled. What per cent were good? 

8. Find the standing of each team for 1928. Re¬ 
arrange the teams in each league in order of standing, 
placing the highest at the top. 

American League National League 


Team 

Won 

Lost 

Team 

Won 

Lost 

Boston 

57 

96 

Brooklyn 

77 

76 

New York 

101 

53 

Philadelphia 

43 

109 

St. Louis 

82 

72 

New York 

93 

61 

Cleveland 

62 

92 

Pittsburgh 

85 

67 

Detroit 

68 

86 

Boston 

50 

103 

Philadelphia 

98 

55 

Cincinnati 

78 

74 

Chicago 

72 

82 

St. Louis 

95 

59 

Washington 

75 

79 

Chicago 

91 

63 


9. A farmer has an average income of $1600 a year. 
This represents 8% of the sum he invested in the farm. 
How much money is invested in the farm? 

10. Mr. Jackson bought a hundred-acre farm for 
$12,500. He sold it for $15,000. What was the per cent 
gain per acre? 


216 


THE BAYNE-SYLVESTER ARITHMETIC 


146. Problems in Commission 

1. A real-estate agent sold 3 lots for $750, $975, and 
$1025, respectively. What was his commission at 5%? 

2. For selling real estate an agent charges 4|% com¬ 
mission. How much should he receive for selling 5 lots 
at $2250 each? 

*3. A traveling salesman earned $3600 last year, of 
which $1200 was salary. The remainder was his com¬ 
mission at 5% on sales. What was the amount of his 
sales last year? 

4 . A lawyer collected 80% of a debt of $2560 at 5% 
commission. How much did the creditor receive? 

5. Find the net proceeds of a sale of 450 bbl. of pota¬ 
toes at $3.75 per barrel. Commission, 3%. 

6. A fruit grower shipped 1200 baskets of peaches to 

his agent, who sold them at $.75 per basket. The freight 
charges amounted to $45.50; the rate of commission was 
3%. (a) What was the agent’s commission? (b) How 

much did the grower receive? 

7. A commission merchant sold 1240 bu. of wheat at 
$li per bushel. He deducted 50% for commission. 
What were the net proceeds of the sale? 

8. A cotton broker bought 500 bales of cotton for a 
New England mill. The cotton weighed 245,000 lb. and 
sold for 22}4^ per pound. Find the commission at 5%. 

9. I shipped my ageiit 380 bbl. of apples which he 

sold at $2.75 per barrel on a 5% commission, (a) His 
commission was_ (b) the net proceeds were- 

10. An auctioneer sells at auction the following: 2 
chairs at $7.50 each; 3 rugs at $18.75 each; a buffet for 
$39.50. What is his commission at 2%? 




SEVENTH GRADE 


217 


147. Miscellaneous Problems 

1 . How long will it take to travel 1254 mi. by train at 
an average speed of 45.6 mi. per hour? 

2. What must Mr. Sanford pay for 3 carloads of 
brick, each containing 8000 bricks, at $27.50 per thousand? 

*3. How many pint bottles can be filled from 4 cans 
containing 20 gal. each? 

4. What is the area of a rectangular plot of ground 
which measures 18 ft. 6 in. by 100 ft.? 

5. A school buys 180 half-pint bottles of milk daily at 

4^^ a bottle. The milk is sold at 5{z^ a bottle. How 

many additional bottles can be bought with the difference 
between the total cost and the total selling price? 

6. A cubic foot of ice weighs 56.8 lb. How many 
pounds are there in a cake of ice 4 ft. long, 3 ft. wide, and 
Ij ft. thick? 

7. What will 16,250 lb. of coal cost at $14.50 a ton? 

8. Fred worked 26 days for $7.50 a day. He de¬ 

posited 20% of his earnings in the bank. How much did 
he deposit? 

9. John has a camera that takes moving pictures. 
Each separate picture in the reel measures f in. in height. 
How many pictures are in a reel 150 ft. long? 

10. Mr. Wallace’s bill for coal for an apartment house 
amounted to $645 for 60 T. He paid cash and was allowed 
a discount of 10%. At this rate, what was the net cost 
per ton? 

11 . How far will a train travel in 24.5 hr. if the average 
speed is 42.8 mi. per hour? 


218 


THE BAYNE-SYLVESTER ARITHMETIC 


12. Mary works 8 hr. a day for 6 days in the week at 
AQift an hour. If her pay is increased to 45^ an hour, how 
much more will she earn in a week? 

13. A farmer sold 4 loads of hay weighing as follows: 
2 T. 250 lb.; 1 T. 750 lb.; 2 T. 500 lb.; 1 T. 750 lb. 
(a) What was the total weight of the hay? (5) At $10 a 
ton, what did he receive for the hay? 

14. Mr. Brown sold an automobile for $1680. This 
was 70% of the cost. What did the automobile cost him? 

16. A train leaving Cleveland at 8 a.m. reaches Wash¬ 
ington at 10.15 p.M. The distance traveled is 489 mi.* 
What is the average mileage per hour? 

16. The school record for the running high jump is 
6 ft. 5j in. Walter can jump 5 ft. ll| in. How far is he 
below the record? 

17. The owner of a stationery store bought a gross of 
pencils for $4.80. He sold them at 5^ each. What is the 
per cent of profit on the gross? ^ 

18. There are 244,000 Indians in the United States. 
Of this number, 5500 live in New York. What per cent 
live in New York? 

19. A cubic foot of water weighs 62.5 lb. What is the 
weight of the water in a tank with a capacity of 72.8 cu. ft. 
if the tank is only half full? 

20. When Mr. Gordon started on a trip, the speedom¬ 
eter registered 6500.2 mi. After the first day it regis¬ 
tered 6750.8 mi. The next day it registered 6925.1 mi., 
and on the last day it registered 7210 mi. (a) How far 
did Mr. Gordon travel each day? (5) What was the 
average mileage per day? 


SEVENTH GRADE 


219 


21. In 1928, Haldeman and Stinson remained aloft in 
their airplane for 53 hr. 36 min. 30 sec. In the same 
year, Zimmerman in Germany stayed aloft 65 hr. 25 min. 
How much longer did Zimmerman remain in the air than 
Haldeman and Stinson? 

22. A dealer buys blank books for 4f each and sells 
them at 8^ each. What does he make on 10 doz. books? 

23. Mrs. Waldon ordered a dozen apples at the rate of 
4 for 15jzf, 1| doz. oranges at 60^ a dozen, and ^ doz. 
bananas at 3j^ each. How much change should she 
receive from $5? 

24. A farmer planted 60 A. in wheat. The yield was 
35.5 bu. per acre. At $1.45 a bushel, what did he receive 
for the wheat? 

25. What is the area of a right triangle with a base of 
64^ ft. and an altitude of 27| ft.? 

26. Mr. Stuart built a new barn at a cost of $1250. 
He paid $750 down and agreed to pay $250 semiannually 
until the barn was paid for. How long will it take him 
to pay for the barn? 

27. A commission merchant sold 1250 bu. of wheat at 
$1.15 a bushel and 500 bii. of oats at $.80 a bushel. He 
deducted 5% and sent a check to his client for the balance. 
What was the amount of the check? 

28. What is the area of a triangular garden plot having 
one square corner, a base measuring 12 ft., and an alti¬ 
tude of 12 ft.? 

29. Mr. Wallace borrowed money on June 15, 1929, 
and paid it back on May 20, 1930. How long did he 
have the money? 


220 


THE BAYNE-SYLVESTER ARITHMETIC 


148. Step-by-Step Test Drill—^ Application of 
Percentage. I 




A 

B 

C 

D 

E 

1 . 

Cost 

$5000 

$12,000 

$8000 

$15,000 

$16,000 


Rate of Gain 

200% 

100% 

100% 

300% 

200% 


Selling Price 

? 

? 

? 

? 

? 

2. 

Amount of Sale 

$50,000 

$26,500 

$18,000 

$20,000 

$64,000 


Rate of Commission 

21% 

5i% 

31% 

4i% 

51% 


Net Proceeds 

? 

? 

? 

? 

? 

3. 

Cost 

$5250 

$6400 

$18,000 

$24,000 

$18,600 


Selling Price 

$3150 

$4800 

$2250 

$15,000 

$12,400 


Rate of Loss 

? 

? 

? 

? 

? 

*4. 

Amount of Sale 

$600 

$800 

$1000 

$2000 

$2400 


Net Proceeds 

$570 

$760 

$900 

$1960 

$2328 


Rate of Commission 

? 

? 

? 

? 

? 

*6. 

Gain 

$200 

$1600 

$5200 

$1600 

$1800 


Per Cent of Gain 

621% 

161% 

40% 

25% 

37§% 


Cost 

? 

? 

? 

? 

? 

*6. 

Commission 

Per Cent of Com¬ 

$40 

$36 

$400 

$300 

$600 


mission 

5% 

9% 

2% 

4% 

3% 


Amount of Sale 

? 

? 

? 

? 

? 

7. 

List Price 

$75 

$200 

$1600 

$3200 

$1400 


Discount 

33i% 

12% 

25% 

8% 

75% 


Net Price 

? 

? 

? 

? 

? 

*8. 

list Price 

$2.50 

$6.00 

$6.25 

$25.00 

$120 


Net Price 

$1.50 

$3.75 

$4.00 

$17.50 

$90 


Per Cent of Discount 

? 

? 

? 

? 

? 

9. 

List Price 

$600 

$940 

$7000 

$8000 

$14,000 


Discounts 

3%, 

8% 

20%, 

5% 

25%, 

5% 

10%, 

5% 

15%, 

10% 


Net Price 

? 

? 

? 

? 

? 



















SEVENTH GRADE 


221 


149. Step-by-Step Test Drill — Application of 
Percentage. II 




A 

B 

c 

D 

E 

1. 

Principal 

$380 

$470 

$286 

$184 

$282 


Rate 

6% 

7% 

5% 

5% 

4% 


Time 

2 yr. 

3yr. 

6 yr. 

3 yr. 

4 yr. 


Interest 

? 

? 

? 

? 

? 

2. 

Principal 

$340 

$234 

$2500 

$5580 

$3500 


Rate 

6% 

5% 

4% 

3% 

5% 


Time 

2 yr. 6 mo. 

1 yr. 6 mo. 

2 yr. 3 mo. 

2 yr.lOmo. 

1 yr. 4mo. 


Amount 

? 

? 

? 

? 

? 

3. 

Principal 

$4250 

$10,500 

$7500 

$10,800 

$12,300 


Rate 

6% 

6% 

6% 

6% 

6% 


Time 

30 da. 

30 da. 

30 da. 

30 da. 

30 da. 


Amount 

? 

? 

? 

? 

? 

4. 

Principal 

$720 

$3200 

$6500 

$3600 

$690 


Rate 

4% 

4% 

4% 

4% 

4% 


Time 

30 da. 

30 da. 

30 da. 

30 da. 

30 da. 


Amount 

? 

? 

? 

? 

? 

6. 

Principal 

$3663 

$4242 

$6200 

$2400 

$3600 


Rate 

6% 

6% 

6% 

6% 

6% 


Time 

60 da. 

60 da. 

60 da. 

60 da. 

60 da. 


Amount 

? 

? 

? 

? 

? 

6. 

Principal 

$4242 

$6200 

$24Q0 

$3600 

$3663 


Rate 

6% 

6% 

6% 

6% 

6% 


Time 

90 da. 

90 da. 

90 da. 

90 da. 

90 da. 


Amount 

? 

? 

? 

? 

? 

7. 

Principal 

$1350 

$2500 

$720 

$1280 

$1850 


Rate 

4% 

4% 

4% 

4% 

4% 


. Time 
Quarterly 
Compound 

1 yr. 

1 yr. 

1 yr. 

1 yr. 

1 yr. 


Interest 

? 

? 

? 

? 

? 

















222 


TliE BAYNE-SYLVESTER ARITHMETIC 


150. Same — Different Test 

Read each pair of statements. If they are the same, write 
‘^Same.’^ If they are different, write “Different.” 

Example: 



nf fin 

Sa.mp! 

J of 60 


nf BO 

Different 

2.5 X 60 

1. 

2 5 


7 

Q 

2. 

4 0 

5|% of $6000 


O 

5.5 of $6000 

3 . 

4 . 

?inn% nf 70 


.3 X 70 

9, qt,. 


50% of 1 gal. 

5 . 

87 ft, 


29 yd. 

6 . 

f hr. 


40 min. 

7 . 

8 . 

112i% of 2400 


f X 2400 

^44 i^q in. 


1 sq. yd. 

9 . 

4.5% of 632 


.045 X 632 

10. 

F. V .fBOon 


500% of $5000 

11. 

37i% of 850 


1 of 850 

12. 

f of 64 


.75 of 64 

13 . 

150% of 650 


.15 X 650 

14 . 

5280 ft. 


1760 yd. 

15 . 

5 of 1 T 


1000 lb. 

16 . 

16|% of 3000 


.66f X 3000 

17 . 

,3 sq. ft- 


1 sq. yd. 

18 . 

1 -.5 hr- 


90 min. 

19 . 

83|% of 2400 


1 of 2400 

20. 

75% of $480 


$360 

21. 

100 X 596 


5960 































SEVENTH GRADE 


223 


22. .78_780 ^ 1000 

23. .0325 X 100 _3j% of 100 

24. 62^% of 1600_I of 1600 

25. 7.5 X 500 _ .7i X 500 

151. Completing Sentences 

1. To find the interest on a given sum, I must know 

the_,_, and_ 

2. To find the net proceeds, I subtract the_from 

the_ 

3. There are two kinds of bank accounts, _ and 


4. Expenses that are necessary to carry on a business 

are called_ 

5. Money received for services on a weekly, monthly, 

or yearly basis is called a_ 

6. Money received for executing an order or selling 

goods is called_ i 

7. The principal plus the interest is called the_ 

8. A plan for spending money is called a_ 

9. The amount of money a family has to live on is 

called the_ 

10. The amount of money that is left to your account 

in a bank is called the_ 

11. When goods are bought for less than the list price, 

they are bought at a- 

12. A triangle with a right angle is called a_ 

13. A four-sided figure with four right angles is called 

a_ 

14. When a small line is used to represent a long line, 

the drawing is made- 










224 


THE BAYNE-SYLVESTER ARITHMETIC 


152. Foreign Money 

American manufacturers and merchants have estab¬ 
lished an extensive trade with many foreign countries, as 
you have learned from your study of geography. Ameri¬ 
can imports and exports run into vast sums yearly. This 
is especially true with respect to certain European coun¬ 
tries. 

Again, many Americans travel abroad each year, and 
many foreigners visit our land. 

In our trading with foreign lands, it becomes necessar}' 
for us to exchange United States money for foreign money. 
For example, in trading with England, United States 
money must be exchanged for its equivalent in value in 
English money. An American about to travel in France 
would exchange his money for French money. Therefore, 
it is necessary for us to learn something of the money 
systems of certain foreign countries. 

United States money is based upon the decimal system. 

10 cents = 1 dime. 

10 dimes = 1 dollar. 

Instead of learning the above table, the English school¬ 
boy learns: 

12 pence (d.) = 1 shilling (s.) 

20 shillings = 1 pound (£) 

The English penny is worth approximately 2(ji\ the 
English shilling is worth approximately 25^ (24.33^); the 
English pound is worth approximately $5 ($4.8665). 

*What is the approximate value in United States money 
of 2 s.? Of 5 s.? Of 10 s.? 

*What is the value of the English £? 


SEVENTH GRADE 


225 


The French schoolboy learns: 

100 centimes (c.) = 1 franc (fr.) 

Before the World War, the franc was equivalent in value 
to about 20^^ of our money ($.193). This was its par 
value. Today, the franc is worth about 4jz^. This is its 
exchange value. 

* About how many francs would you receive today in 
exchange for a dollar bill? 

* What is the approximate value today of 10 fr.? Of 
50 fr.? 

The German schoolboy learns: 

100 pfennig (pf.) = 1 mark (M.) 

The German mark today is worth about 25^ ($.2382). 

* What is the approximate value of 10 M. in our money? 
Of 50 M.? 

* About how many marks would you receive in exchange 
for $2? For $10? 

The Italian schoolboy learns to use the lira, a coin which 
is equivalent to about 5^ of our money ($.05236). A one- 
dollar bill, then, could be exchanged for-lire. 

* What is the approximate value of 5 lire? Of 40 lire? 

* About how many lire would you receive in exchange 
for $2? For $5? 


Country 

England 

France 

Germany 

Italy 


Table of Equivalents 


Unit 

Exact Value 

Approximate Value 

shilling 

$ .2433 

$ .25 

pound 

$4.8665 

$5.00 

franc 

$ .039179 

$ .04 

mark 

$ .2382 

$ .25 

lira 

$ .05236 

$ .05 


226 


THE BAYNE-SYLVESTER ARITHMETIC 


*153. Problems 

1 . An American merchant paid a French manufacturer 

50 fr. each for lace collars. • Each collar would be worth 
about _ in United States money. 

2. A certain book is sold in Paris at the cost of 10 fr. 
What would it cost in our money? 

3. A traveler paid 10 M. for a German book. It 

would cost_in United States money. 

4 . An American traveling in England exchanged $25 

for English money. He received about_ 

6. Mr. Johnson bought an overcoat in London for £5. 

That would be equivalent to about _ in United States 

money. 

6. In a .certain shop in Rome, copies of famous paint¬ 

ings were sold at 1000 hre each. In our money they 
would cost $_ 

7. An Englishman exchanged £200 for United States 
currency. How much did he receive? 

8. One dollar of our money is worth about_fr. in 

Paris; _M. in Berlin;_lire in Italy. 

9. Flora Jones wrote to her cousin Jeanne in Paris: 
“I have a new copy of Alice in Wonderland, which cost 

two dollars.” Jeanne thought, “Flora paid _ fr. for 

her book.” 

10. Complete this table: 

Approximate Value in 

Country Coin or Note Abbreviation U. S. Money 

France 


pound 

lira 


M. 









SEVENTH GRADE 


227 


154. Taxes 

Every child who has studied American history knows 
that the cry of ^‘No taxation without representation’’ 
had a great deal to do with the Revolutionary War. 
Every father or mother who owns property or who has an 
income has talked about taxes. People who come back 
to America from foreign countries meet a customs officer 
who looks over what is brought in to see whether a duty 
should be paid. Let us see what taxes mean and what 
they have to do with us as individuals. 

We live in a great city. We see about us policemen, 
firemen, street cleaners, and many others who are em¬ 
ployees of the city. We go to a public school where we 
find teachers and principals and where we are furnished 
with textbooks and supplies. We go through the streets 
and find them being repaved and lighted. We go into 
our homes and find water supplied in our apartments and 
houses. We hear of a mayor, of a judge, of dock depart¬ 
ments, bank departments, health departments, hospitals, 
prisons, and of a number of other city activities. Do we 
always stop to think how these are paid for? We say the 
^^city” pays for them. That is true, but the city govern¬ 
ment cannot get its money for these activities except 
through its citizens. This means that your parents and 
all other members of the community must raise the money 
necessary to provide these advantages. This money is 
raised by taxation, and the different forms of raising it are 
called taxes. 

Every year our city government makes a careful esti¬ 
mate of how much money will be needed to carry on the 
work of the government for the following year. This is 


228 


THE BAYNE-SYLVESTER ARITHMETIC 


called making the city budget. Each department of the 
government, education, police, health, fire, and so on, 
has a separate estimate made for its needs. The sum of 
all these estimates for all the departments of government 
is called the budget. The city now has to plan how to 
raise this money by taxes. Taxes for the city are generally 
a per cent of the estimated value of real property and per¬ 
sonal property. 

Real property means land and the buildings on it. 

Personal property is movable property such as furniture, 
mortgages, or live stock. 

The tax rate is a very important matter. Lowering or 
raising it means much to the taxpayer. Let us see how 
the tax rate is found. 

Suppose that a small town plans a budget of $21,000 
for next year. This means that $21,000 must be raised 
by taxation. Since the amount raised by taxes on per¬ 
sonal property is usually small, we shall calculate how 
the whole amount could be raised on the real estate of the 
town. The tax assessor estimates the value of all the real 
estate of the town at $875,000. - Then $21,000 must be 
raised on $875,000. 


21000 

875000 


21 

875 


= .024 = tax rate 


This may be read as 24 mills on each dollar of assessed 
valuation, or as $2.40 on each hundred dollars, or as $24 
on each thousand dollars. 

A property owner whose property is assessed at $1000 
would pay $24; one whose property is assessed at $2000 




SEVENTH GRADE 


229 


would pay $48 tax. How much would one whose property 
is assessed at $1500 pay? One whose property is assessed 
at $5000? One whose property is assessed at $7500? 
One whose property is assessed at $20,000? 

155. Problems 

1 . The tax rate is $1.84 per hundred. How much tax 
must a man pay on property assessed at $35,500? 

2. Property worth $60,000 is assessed at | of its real 
value. What will the tax amount to if the rate is $.015 
on the dollar? 

3. The value of Mr. Henry’s property is $45,000. 
How much will the tax be if the rate is$18.50 per thousand? 

4. Three years ago the assessed valuation of property 
in a town was $750,000. This year it is $810,000. The 
tax rate for both years was $.025 per dollar. How 
much more in taxes was raised this year than three years 
ago? 

*5. A man owns property valued at $50,000. In 1925 
it was assessed at 60% of its value. The tax rate in 1925 
was $20.50 per thousand. In 1929 it was assessed at 75% 
of its value. The tax rate in 1929 was $19.50 per thou¬ 
sand. In which year were his taxes higher, and how 
much higher were they? 


6. Find the tax on each of the following: 



Value of Property 

Assessed at 

Rate per hundred 

(a) 

$120,000 

90% of value 

$1.42 

W 

$65,000 

60% of value 

$2.40 

(c) 

$7,000 

100% of value 

$1.54 

(d) 

$82,000 

75% of value 

$1.76 

(e) 

$38,000 

70% of value 

$2.02 


230 


THE BAYNE-SYLVESTER ARITHMETIC 


156. United States Government Taxes — 
Customs and Duties 

Our national government must raise money for its 
various activities just as the state and the city do. It does 
not tax real estate, however, but levies taxes on other 
things. It raises great sums on the incomes of individuals 
and corporations. Persons with smaller incomes pay not 
only less but at a lower rate than persons with large in¬ 
comes. The national government also levies taxes on 
goods imported into the United States from foreign coun¬ 
tries. You have learned something about this kind of 
tax from your history, particularly from discussions of 
the tariff. Taxes on goods imported from other countries 
are called customs or duties. They are levied either to 
raise money to support the government or to prevent 
poorer-paid foreign workmen from selling goods at such 
low prices in our country that our better-paid American 
workmen would be thrown out of work or forced to ac¬ 
cept lower wages. 

Duties or customs are not levied on all imported goods. 
Some goods are admitted free. Goods that are taxed 
may be divided into three classes: 

1. Goods taxed on their cost or value. Such goods are 
subject to an ad valorem duty, which is a certain per cent 
of the value of the goods as stated in their invoice. 

2. Goods taxed according to quantity; that is, a certain 
amount per yard or per pound. This is called specific 
duty and does not consider the value of the goods. 

3. Goods that are subject to both an ad valorem and a 
specific duty. 


SEVENTH GRADE 231 

State which kind of duty is levied in each of the following 
cases: 

1. The duty on bacon is 2(^ a pound. 

2. The duty on corn is 15^ a bushel. 

3. Lace is subject to a duty of 90% of its value. 

4. Barley is subject to a duty of 20^2^ a bushel. 

6. Cotton cloth is subject to a duty of from 10% to 
45% of its value. 

6. The duty on lard is 1^ per pound. 

7. Wool blankets are subject to duty as follows: from 
30% to 40% of value and 18^ to 37^ a pound, depending 
on the quality. 

8. On Oriental rugs the duty is 55% of the value. 

9. Printing paper is subject to a duty of 10% of the 
value and a pound. 

10. The duty on scissors is 45% of the value and from 
3^^ to 20^ each. 

157. Using Graphs for Comparisons 

Construct graphs from the information given: 

1. The value of the rubber imported by the United 
States from certain countries in one year was as follows: 

Brazil $12,000,000 Dutch East Indies $87,000,000 

Ceylon $45,000,000 Malaya $315,000,000 

2. The value of the silk imported from China by one 
country in one year was $50,000,000. The value of the 
silk imported from Japan by the same country for the 
same period was $390,000,000. 

3. The following figures show the value of the exports 
to and imports from the countries listed made by the 
United States in one year: 


232 


THE BAYNE-SYLVESTER ARITHMETIC 


Country 

British South Africa 

Australia 

China 

Japan 

Philippine Islands 


Exports 


Imports 


$50,000,000 

$160,000,000 

$85,000,000 

$260,000,000 

$70,000,000 


$10,000,000 

$40,000,000 

$150,000,000 

$400,000,000 

$115,000,000 


158. Problem Analysis 


1. Before attempting to solve the problem, read it 
carefully. 

2. Ask yourself: 

(а) What facts are given? 

(б) What am I to find? 

(c) What is the first step? How shall I solve it? 

(d) What is the next step? How shall I solve that? 

(e) Are there any more steps? 

(/) What is a reasonable answer? 

3. Work the problem step by step. Check your 
answer. 

1. What will it cost to excavate a cellar 24 ft. long, 
21 ft. wide, and 12 ft. deep at 75j^ per cubic yard? 

2. A contractor worked on a job which cost him $3600 
to complete. He wished his profit to be 12 of the cost. 
What did he charge the man who employed him in order 
to make this profit? 

3. What is the per cent of gain on silk bought at $1.50 
a yard and sold at $2.25 a yard? 

4. A farmer sells his produce through a commission 
merchant who charges 10% commission. What will the 
farmer receive for a load of produce which sells for $500? 


SEVENTH GRADE 


233 


6. A mechanic earns 13640 a year. He saves 12^% 
of his money. At this rate, how much will he save in 
4 years? 

6. Find the cost of railroad tickets for a family of 5 
adults for a trip 800 mi. long at 3^^ a mile. 

7. The list price of an article is $46.50. It is marked 
down 40%. What must I pay for it? 

8 . (a) How many feet of chicken wire are needed to 
inclose a garden 49^ ft. wide and 62^ ft. long? (b) At 
12^ a yard, what will it cost to inclose the plot? 

9. The governor of a state receives $25,000 a year. 
The mayor of a city in that state receives $45,000 a year. 
What per cent of the mayor’s salary is the salary of the 
governor? 

10. Frank left for the country on the 9.20 a.m. train. 
He reached his destination at 12.15 p.m. How many 
minutes did he spend on the train? 

11. The distance from New York to Boston by boat is 
305 nautical miles. A nautical mile is equivalent to 1.152 
statute miles. What is the distance in statute miles? 

12. The distance from Chicago to Washington is 874 
miles. The trip is made in 28.5 hr. What is the average 
mileage per hour? 

13. Mr. Wilson borrowed $8000 from the bank on 
February 1, 1930. He paid it back with interest on 
September 1, 1930. How much did he return to the bank? 

14. The assessed valuation of real estate in a town is 
$250,000. If the budget is estimated at $20,000, what 
will the tax rate be? 

*15. A clerk saves 8% of his salary. If his savings 
amount to $12 per month, how much does he earn in a 
year? 


234 


THE BAYNE-SYLVESTER ARITHMETIC 


159. Supplying the Question 

Example: A train leaving at 1.15 reaches its destination 
at 1.45. The distance is 18 mi. 

(a) How long did it take to make the trip? 

(5) At that rate, how far would the train travel in an 
hour? 

(c) What is the average speed per minute? 

(d) About how many miles have been traveled at 1.30? 

Complete each problem by supplying a question. Then 
solve the problem: 

1. The catalogue price of an article is $24.50. The 
cash purchaser is allowed 20% discount. 

2. A house which was bought for $11,500 was sold for 
$15,000. 

3. Mr. Edward’s average sales amount to $2500 a 
week. He receives 8% commission. 

4. An agent sold Mr. Brown’s 125-acre farm at $75 
an acre. He charged 5% commission. 

5. Mr. Baird borrowed $1500 from the bank for one 
year at 6%. 

6. A farmer with a 250-acre farm planted 75 acres in 
wheat. 

7. In a recent election, 125,000 persons were entitled 
to vote. Only 85,000 voted. 

8. There were 480 pupils enrolled in a summer school. 
Of this number, 85% were promoted. 

9. Mr. Spear invested $15,000 and earned a profit of 
$675. Mr. Barrows invested $12,500 at a profit of $650. 

10. Gold production in the United States dropped from 
about $101,000,000 in 1915 to about $45,100,000 in 1927. 


SEVENTH GRADE 


235 


160. Approximating Answers 

Example: The catalogue price for a lawn mower is 
$12.50. A special discount of 10% was allowed Mr. Ford. 
What was the net price? 

$11.25 $10 $1.25 $13.75 

Think: 10% of $12.50 = $1.25; $12.50 - $1.25 = 

$11.25. 

In the following problems^ select from the four answers the 
one which is right: 

1. A dealer allowed a farmer 10% off for paying cash 
for his reaper. The discount amounted to $14.50. What 
was the regular price? 

$145 $1450 $160 $130.50 

2. Find the area of a right triangle with a base of 45 ft. 
and an altitude of 20 ft. 

900 sq. ft. 450 sq. ft. 200 sq. ft. 810 sq. ft. 

3. A man bought a lot for $1500 and sold it for $3000. 
What was the gain per cent? 

30% 10% 15% 100% 

4. An article bought for $2.40 was sold at a discount of 
12^%. What was the selling price? 

$12.50 $2.10 $1.60 $2.70 

6. A real-estate dealer sold a house for $24,000. His 
commission rate was 4%. How much money was due 
the owner? 

$23,040 


$20,000 


$24,960 


$960 


236 


THE BAYNE-SYLVESTER ARITHMETIC 


161. Selecting the Operation 

From the three suggested solutions select the one that is 
correct, and on a paper write it after the number of the problem: 

1. An agent collected 75% of a debt amounting to 
S9000. How much did he collect? 

75 X S9000 f of 19000 7.5 X 19000 

2. For what price must a merchant sell a coat that costs 
175 in order to gain 33f%? 

.33| X $75 33§ X $75 $75 + of $75) 

3. A stationery dealer buys pencils at $4.50 a gross and 
sells them at 5^ each. How much does he make? 

$4.50 - (12 X $.05) (144 X $.05) - $4.50 $4.50 ^ 144 

4. A record for the running high jump is 6 ft. 5 in. 
Fred can jump 5 ft. 8 in. How much higher must he 
jump before he reaches the record? 

6 ft. 5 in. — 5 ft. 8 in. 5X8 in. 

5 ft. 8 in. + 6 ft. 5 in. 

5. At $.60 an hour, what will a man receive for working 
35 hr. and 45 min.? 

(35 + 45) X $.60 35 X $.60 35j X $.60 

6. Find the interest on $900 for 1 year 3 months at 4%. 

X f X $900 $900 X 5 X T^o -04 X $900 + J 

7. Wages in a factory were reduced 12^%. What will 
a man receive whose wages were $16 a day before the cut? 

.12J X $16 I X $16 $16 - (.08 X $.16) 


SEVENTH GRADE 237 

8. How many quarter-pound packages can be made 
from 8 lb. of tea? 

8-j-J Jof8 8Xj 

9. An aviator who flies to an altitude of 2.2 mi. has 
risen how many feet? 

2.2 X 1780 2.2 X 5280 2| X 5280 

162. Changing the Wording of Problems 

Example: What is the interest on $6000 for 1 year 
at 6%? 

(а) $6000 loaned for 1 year at 6% will earn_ 

(б) The rate is 6%; the time, 1 year; the principal, 
$6000. What is the interest? 

Try to vary the wording of the following problems in as 
many ways as possible: 

1 . A cubic foot of water weighs 62.5 lb. What will 
12^ cu. ft. weigh? 

2. Mr. Mead bought a house for $12,600 and sold it 
for $15,000. What was the rate of gain? 

3. Railroad fare is $.035 a mile. Find the cost of a 
ticket for a trip of 360 mi. 

4. A man’s yearly salary is $4200. What is his 
monthly salary? 

5. Mr. Ward has a yearly income of $5000. He 
budgets his income, setting aside 30% for food. How 
many dollars does he allow for food? 

6. A dress marked $27.50 was offered for sale at a 
reduction of 20%. What was the selling price? 

7. A man’s yearly salary was raised from $3000 to 
$3500. What was the per cent of increase? 



238 


THE BAYNE-SYLVESTER ARITHMETIC 


8. Mr. Walton invested $13,000 in property which 
brought him an income of $1300 yearly. What was the 
rate of return on his investment? 

9. A holiday sale announcement read: “50 coats, 20% 
off.’^ What was the selling price of the coats if they were 
originally priced at $35? 

163. Problems without Numbers 

In each of the following problems, tell how you would 
solve the problem. Then supply reasonable figures for the 
missing numbers and find the answer: 

1. A desk costing _ is sold at a gain of -%. 

What is the selling price? 

2. Mr. Reid was forced to sell his automobile for-- 

less than he paid for it. This was a loss of-% of the 

cost. What was the cost to Mr. Reid? 

3. A school team played_baseball games and 

won_What per cent of the games did it win? 

4. Mrs. Robinson’s gas meter read - on May 1 

and _ on June 1. At _^_ per thousand, what will 

her gas bill amount to? 

5. What is the average weight of - packages, 

weighing_lb.,_lb.,_lb., and-lb., respec¬ 

tively? 

6. Mary’s weekly deposits in the school bank were as 

follows: _, _, _, _,_What was her 

average deposit per week? 

7. Mr. Dure drove his automobile_miles on- 

gallons of gasoline. What was the average mileage per 
gallon? 

8. Mr. Roberts bought an automobile in 1924 for -- 

A few years later he traded it in for a new car that cost 





















SEVENTH GRADE 


239 


_He gave the old car and_in cash. What was 

he allowed for the old car? 

9. Mr. Moffat built a concrete walk in front of his 

property. It was_ft. wide and_ft. long. The 

cost was_per square foot. What was the total cost? 


164. Silent Reading of Problems 

After each problem you will find a question followed by 
four answers. Select the correct answer: 

1. Mr. Stevens ordered groceries from a wholesale 
dealer to the amount of $750. He paid cash and was 
allowed 6% discount. What did he have to pay for the 
goods? 

Which of the following facts are given? 

(а) The amount of the discount. 

(б) The price Mr. Stevens paid. 

(c) The rate of discount. 

{d) The number of articles bought. 

2. Mrs. Ward loaned $250 for 2 years at 6%. How 
much will the principal earn for her? 

Which of the following are you asked to find? 

(a) The interest earned in 1 year. 

(5) The interest earned in 2 years. 

(c) The amount. 

{d) The interest due semiannually, 

3. Anna earns $5 a week. She budgets her money as 
follows: savings, 50%; amusement, 20%; books and 
supplies, 30%. What sum does she set aside for each 
item? 





240 


THE BAYNE-SYLVESTER ARITHMETIC 


Which of the following are you given? 

(а) The number of hours Anna works. 

(б) The amount she spends for books. 

(c) The per cent she saves. 

(d) Anna’s earning per day. 

4. A real-estate agent charges 5% for selhng property. 
What price must he ask for the property in order to get a 
commission of $100? 

Which of the following are you asked to find? 

(a) The commission. 

(b) The cost of the property. 

(c) The price the agent must ask for the property. 

(d) The amount the owner will receive. 

5. Is it better to be allowed J off on a bill amounting to 
$5 or to get a discount of 20% ? How much would you 
save by taking the larger discount? 

Which of the following facts are given? 

(a) The amount saved by taking j off. 

(h) The amount saved by a discount of 20%. 

(c) The amount of the bill. 

(d) The saving by choosing the larger rate. 

6. If an automobile depreciates 18% in value during 
the first year, what will a car that cost $2400 be worth at 
the end of the year? 

Which of the following are you asked to find? 

(а) The amount of depreciation. 

(б) The value of the car after 6 months. 

(c) The cost of the upkeep of the car. 

(d) The value of the car after 1 year. 


SEVENTH GRADE 


241 


166. Contents of Rectangular Solids 

Compare this figure with a candy box, a match box, a 
chalk box. How many sides has it? What shape are 
the sides? 



5 ' 


A solid that has six rectangular sides or faces is called a 
rectangular solid. 

A rectangular solid has three measurements. This solid 
is_in. long, :_in. wide,__ in. high. - 


This solid has_square sides or faces, 

measuring_in. on each edge. 

A solid that is 1 inch long, 1 inch wide, and 
1 inch high is called a cubic inch or an inch cube. 


' = 1 " 


This diagram shows the bottom layer of a candy box 
which is to be filled with caramels. 



Each caramel is an inch cube. 

How many caramels can be placed in one row? 































242 


THE BAYNE-SYLVESTER ARITHMETIC 


How many cubic inches are there in one row? 

How many rows can be placed in the lower layer? 
How many caramels will there be in the lower layer? 
How many such layers will the box hold? 

How many cubic inches will the box hold? 

Another way of saying that a box contains 54 cu. in. is 
to say that its volume is 54 cu. in. 

3 X 6 X 3 = 54, the number of cubic inches 


The volume of a rectangular solid is equal to the 
product of the length, width, and height expressed in 
the same unit of measure. 


The volume of a rectangular sohd is sometimes called 
the cubical contents. 

Use pencil if needed. 

1. How many cubic inches are there in a brick 6 in. by 
3 in. by 4 in.? 

2. How many cubic inches are there in a box 9 in. by 
2 in. by 3 in.? 

3. How many inch cubes can be fitted into boxes with 
these inside measurements? 


Length 

Width 

Height 

(a) 5 in. 

4 in. 

3 in. 

(b) 6 in. 

5 in. 

4 in. 

(c) 4 in. 

3 in. 

2 in. 

(d) 7 in. 

6 in. 

2 in. 

(e) 8 in. 

Tin. 

6 in. 



SEVENTH GRADE 


243 


*4. How many cubic inches are there in (a) a 4-inch 
cube? (6) A 10-inch cube? (c) A 5-inch cube? (d) A 
6-inch cube? (e) A 3-inch cube? 

5. Find the volume of each rectangular solid: 

(a) 5" by 6" by 12" (h) 6" by 12" by 14" 

(c) 12" by 4" by 7" 

6. What is the cubical contents of each of the following 
boxes: 

(a) 12" by 12" by 12" (b) 14" by 8" by 6" 

(c) 12" by 7" by 9" 

Cubical contents or volume may be measured in other 
cubic units than the cubic inch. 

We pay for gas or water by the cubic foot. We speak 
of the number of cubic feet of air allowed each pupil in 
the classroom. Wood is bought and sold by the cord, 
which is equivalent to 128 cu. ft. 

This cube is 1 ft. long, 1 ft. wide, and 1 ft. 
high. It is called a cubic foot. 

To what scale is this cube drawn? Compare 
it with the scale for the drawing of the cubic 
inch. Is a cubic foot larger or smaller than a cubic inch? 

At the blackboard draw a cubic inch. Next to it draw 
a cubic foot, using the exact measurements. 

Without 'pencil. 

7. How many cubic feet are there in a solid 4 ft. long, 
2 ft. wide, and 3 ft. deep? 

8 . A cord of wood is 8 ft. long, 4 ft. wide, and 4 ft. 
high. How many cubic feet does it contain? 

9. What is the volume of a rectangular solid measuring: 

(a) 15 ft. by 2 ft. by 3 ft. (6) 8 ft. by 6 ft. by 2 ft. 

(c) 4 ft. by 6 ft. by 4 ft. 






244 


THE BAYNE-SYLVESTER ARITHMETIC 


Use pencil if needed. 

Find the capacity {cubical contents or volume) of the 
following: 

10. A tank 9 ft. by 12 ft. by II ft. 

11. A tank 8 ft. by 17 ft. by 15 ft. 

12. A bin 12 ft. by 10 ft. by 8 ft. 

13. A bin 15 ft. by 12 ft. by 8 ft. 

14. A bin 20 ft. by 15| ft. by 10 ft. 

15. A freight car 30 ft. by 9 ft. by 8| ft. 

Contractors use a still larger cubic unit for measuring 
the amount of dirt that has been excavated. 

A cubic yard is_yd. long,_yd. wide, and_ 

yard_ 


Find the volume of a solid that measures: 

16. 8 yd. X 5 yd. X 6 yd. 19. 8 yd. by 2 yd. by 3 yd. 

17. 7 yd. X 4 yd. X 2 yd. 20. 5 yd. by 4 yd. by 6 yd. 

18. 4 yd. X 5 yd. X 6 yd. 21. 3 yd. by 8 yd. by 2 yd. 

Often dimensions are not given in the same unit of 

measure. Suppose that we wish to find the cubical 
contents of a bin that measures 8 ft. by 7 ft. by 6 in. 


6 in. = i ft. 

8 X 7 X J = 28, the number of cubic feet 


Change measurements to 
necessary, and find the volume 

22. 6 ft. by 8 ft. by 3 in. 

23. 5 ft. by 4 ft. by 6 in. 

24. 8 in. by 9 ft. by 12 ft. 

25. 8| ft. by 6 ft. by 4 ft. 


the same denomination, if 

26. 4 yd. bj^ 2| yd. by 8 yd. 

27. 8 yd. X 2 yd. X 2 ft. 

28. 12 yd. X 3 yd. X 4 ft. 

29. 6 yd. X 2 yd. X 4 yd. 







SEVENTH GRADE 


245 


30. 2 ft. X 6 yd. X 3 yd. 

31. 7 yd. X 1 ft. X 2 yd. 

32. A room 18 ft. long, 12 ft. 6 in. wide, and 9 ft. high. 

33. A room 24 ft. long, 15 ft. 8 in. wide, 9 ft. high. 

34. A bin 15 ft. 6 in. by 8 ft. 6 in. by 2 ft. 3 in. 

35. A bin 5 yd. 1 ft. by 3 yd. 2 ft. by 2 yd. 

36. A bin 6 yd. 2 ft. by 3 yd. 1 ft. by 3 yd. 

166. Cubic Measure 

The cubic inch, cubic foot, and cubic yard are the 
measures commonly used in finding volume or capacity. 

Often it is necessary, in solving practical problems, to 
change from one unit of measure to another. 

A cubic foot measures 12 inches for all three dimensions. 

12 X 12 X 12 = 1728, the number of cubic inches in 
1 cu. ft. 

A cubic yard is_ft. long,_ft. wide, and_ft. 

high. A cubic yard is equal to_cubic feet. 

1728 cu. in. = 1 cu. ft. 

27 cu. ft. = 1 cu. yd. 


Supply the missing numbers: 


1. 

2 cu. ft. = 

cu. in. 

9. 

f cu. ft. = 

cu. in. 

2. 

\ cu. ft. = 

cu. in. 

10. 

f cu. ft. = 

cu. in. 

3. 

\ cu. ft. = 

cu. in. 

11. 

1 cu. ft. = 

cu. in. 

4. 

cu. in. 

= 3 cu. ft. 

12. 

I cu. ft. = 

cu. in. 

6. 

cu. ft. 

= 2 cu. yd. 

13. 

5 cu. yd. = 

cu. ft. 

6. 

81 cu. ft. = 

cu. yd. 

14. 

cu. ft. = 2j 

cu. yd. 

7. 

36 cu. ft. = 

cu. yd. 

15. 

5§ cu. yd. = 

cu. ft. 

8. 

8 cu. yd. = 

cu. ft. 

16. 

4f cu. yd. = 

cu. ft. 


17. Change 16| cu. ft. to cubic inches. 

18. How many cubic yards are there in 428 cu. ft.? 






















246 THE BAY^^E-SYLVESTER ARITHMETIC 

167. Problems 

Wbat is the cost of excavating a cellar 16 ft. by 18 ft. by 
12 ft. at 70^ a cubic yard? 


A. 1st Step. 16 X 18 X 12 = 3456, number of cubic feet 
excavated 

2nd Step. 3456 27 = 128, number of cubic yards 

excavated 

3rd Step. 128 X $.70 = $89.60, cost of excavating 


2 4 

B. 1st Step. = 128, number of cubic yards 

2nd Step. 128 X $.70 = $89.60, cost of excavating 


In B, the dimensions of the cellar in feet were divided 
by the dimensions of a cubic yard expressed in feet. 

1 . How many cubic yards of earth were removed in 
digging a cellar 18 ft. long, 12 ft. wide, and 8 ft. deep? 

2. What is the capacity of a tank 18j ft. by 15 ft. by 
16j ft.? 

3. How many cubic yards of earth were removed in 
digging a trench 28 ft. long, 6 ft. deep, and 4 ft. wide? 

4. It costs $2 per load to draw gravel. If the dimen¬ 
sions of the wagon are 9 ft. by 3 ft. by 2 ft., what is the 
cost per cubic yard? 

6. A contractor charged $.55 per cubic yard for exca¬ 
vating a cellar 25 ft. by 15 ft. by 12 ft. What was the 
cost of excavating? 





SEVENTH GRADE 


247 


6. How many cubic feet of cut stone and concrete 
are there in a wall 18 ft. long, 12 ft. high, and 3| ft. wide? 

*7. How many cubic feet of water are there in a swim¬ 
ming tank 35 ft. long, 25 ft. wide, and 8 ft. 8 in. deep when 
the tank is f full? 

8 . (a) The excavation for an office building is 90 ft. X 
75 ft. X 24 ft. How many cubic yards of earth were 
removed? (b) The contractor’s price was $.75 a cubic 
yard. What was the cost of removing the earth? 

9. A tank measures 30 ft. by 8 ft. by 5J ft. What 
is its capacity? 

*10. What is the cost of digging a trench 32 in. wide, 
44 in. deep, and 650 yd. long at 75^ per cubic yard? 

*11. What will it cost, at 42^ per square foot, to lay 
a floor in a room 24 ft. 6 in. by 18 ft. 4 in.? 

12. The excavation for the cellar of a bungalow is 34 ft. 
long, 26 ft. wide, and 8| ft. deep, (a) How many cubic 
yards of earth were removed in making the excavation? 
(6) If the contractor’s price was 75^ per cubic yard, 
what was the cost of removing the earth? 

13. How many cubic feet are there in a storage bin 
20 yd. long, 14 yd. wide, and 8 ft. high? 

*14. If there are 36 cu. ft. in a ton of coal, how many 
tons can be stored in a bin 14' X 10' X 8'? 

16. In removing stone from a quarry, an excavation 
250 ft. long, 110 ft. wide, and 48 ft. deep was made, 
(a) How many cubic feet of stone were removed? (b) How 
many cubic yards? 

16. Find the capacity of a packing case the inside 
dimensions of which are 6 ft. 6 in. by 4 ft. 6 in. by 3 ft. 

*17. How many cubic feet are there in a ^concrete 
dam 40 yd. long, 10 ft. 4 in. high, and 22 in. thick? 


248 


THE BAYNE-SYLVESTER ARITHMETIC 


168. Denominate Number Race 

Can you score 100% on this test? Compete row against 
row. The score is the number right. The row having 
the highest average score wins. 


Supply the missing numbers: 
A 

1. 2 mi. =_- ft. 

2. 1 sq. ft. 24 sq. in. =-sq. in. 

3. _cu. in. = 1 cu. ft. 

4. _ft. = I mi. 

5. 1.5 cu. ft. =_cu. in. 

6. \ sq. yd. =-sq. ft. 

7. .5 mi. =_rd. 

8. _cu. yd. = 81 cu. ft. 

9. 2 cu. yd. =-cu. ft. 

10. __ sq. ft. = 3 sq. yd. 

11. 3250 lb. =_ton 

12. \ cu. ft. =-cu. in. 

13. _yd. = i mi. 

14. 26 qt. =_gal. 

15. 3 T. 5 cwt. =_lb. 

16. 1 score =- 

17. _rd. = 11 yd. 

18. _units = 1 gross 

19. .5 hr. =_min. 

20. f da. =-hr. 

21. 3 sq. ft. =-sq. yd. 

22. _da. = 1 leap year 

23. 1 qt. = -gi. 

24. 21 T.* =_lb. 

26. 2 mi. = _rd. 


B 

2 rd. =_ft. 

1 sq. mi. =-A. 

3 cu. yd. =-cu. ft. 

_rd. = 1 mi. 

12 sq. ft. =_sq. in. 

_cu. yd. = 135 cu. ft. 

i sq. ft. =_sq. in. 

_gal. = 46 qt. 

_cu. ft. = 1 cu. yd. 

1 sq. yd. + 7 sq. ft. = 

_sq. ft. 

_rd. = I mi. 

_pt. = 2 gal. 

_oz. = 6J lb. 

5 sq. yd. =-sq. ft. 

12\ doz. =_pencils. 

_cwt. = 800 lb. 

1 rd. =_ft. 

1 gross =_doz. 

_min. = If hr. 

5 cu. ft. =_cu. in. 

I yr. =-mo. 

18 cu. ft. =-cu. yd. 

_yr. = 10 mo. 

IJ sq. ft. =_sq. in. 

5i qt. =-pt. 




















































SEVENTH GRADE 


249 


169. A Holiday in the South 


The Rogers family of five took a trip to the South for a 
holiday this winter. Look at the map and tell how they 
traveled from place to place. 

1. Mr. Rogers bought tickets for all his family for the 
trip from New York to Jacksonville, at $36.55 each. 


(a) What did he pay 
for tickets? Since 
they spent one night 
on the train, he had to 
get sleeping accommo¬ 
dations. He reserved 
a compartment at 
$30.75 and two lower 
berths at $10.88 each. 
Meals on the train 
averaged $3 a day for 
each person, (b) What 
was the total cost of 
the railroad trip? 

2. They left New 
York at 9.40 a.m. and 
reached Jacksonville 
at 9 A.M. the next day. 
make the trip? 


‘‘fJew York 



How many hours did it take to 


3. Elsie looked at the time-table and noticed that their 
train stopped at these cities: New York, Jersey City, 
Newark, Philadelphia, Wilmington, Baltimore, Washing¬ 
ton, Richmond, Charleston, Savannah, and Jacksonville. 
Through which states did they pass? 




^50 THE BAYNE-SYLVESTER ARITHMETIC 

4. The train passed over the lines of three railroads. 
The following figures show the mileage on each road; 

I II HI 

New York 0 mi. Washington 0 mi. Richmond 0 mi. 
Philadelphia 91 mi. Richmond 114 mi. Charleston 399 mi. 
Baltimore 187 mi. Jacksonville 681 mi. 

Washington 227 mi. 

(а) Find the total mileage on each road. 

(б) Find the total distance from New Y ork to J acksonville. 
(c) When they reached Charleston, how much of the 

journey remained? 

5. What is the average mileage per hour 
from New York to Jacksonville? 

The Automobile Trip 

This diagram shows the road map the 
Rogers family followed from Jacksonville 
to Miami. They planned to travel only 
hours each day. 

1. On the first day they went as far as 
New Smyrna, (a) How far did they 
travel? (b) WJiat was the average mile¬ 
age per hour? 

2. The second day they reached Ft. 
Pierce. What was the average mileage 
per hour for that day? 

3. What was the average mileage per 
hour for the last day? 

4. (a) What was the total distance 
traveled by automobile? (6) What was 
the average daily mileage? 





SEVENTH GRADE 


251 


6. When they had reached Daytona, about what part 
of the trip did they still have to make? 

6. At Titusville, how many miles remained to be 
traveled? 

7. Which is nearer Miami — Melbourne or Daytona? 
How much nearer is it? 

8. How far is it from Jacksonville to (a) Daytona, 
(b) Palm Beach, (c) Miami? 

9. The gasoline cost 24^ a gallon. Mr. Rogers used 
19 gal. (a) What was the average mileage per gallon? 
(b) What was the average cost per mile? 

10. Make up a problem about distances between cities. 


The Airplane Trip 

This is the schedule followed by the Rogers family on 
their airplane trip: 


Leave 

1st day Miami 9.15 a.m. 

2nd day Havana 12.15 p.m. 

3rd day Camaguey 3.45 p.m. 
4th day Santiago 7 a.m. 

5th day Port an Prince 10.30 a.m. 
6th day Santo Domingo 1 p.m. 


Arrive Distance 

Havana 11.30 p.m. 245 mi. 

Camaguey 3.15 p.m. 314^ mi. 
Santiago 5.25 p.m. 175 mi. 
Port au Prince 10 a.m. 250 mi. 
Santo Domingo 12.30 p.m. 160 mi. 
San Juan 4 p.m. 2711 mi. 


1. From this schedule find the average mileage per 
hour for each day’s travel. 

2. (a) Find the total mileage. (6) Find the total time 
spent in the air. (c) Find the average mileage per hour 
for the trip. 

3. A ticket from Miami to San Juan costs $245. What 
was the total cost for the Rogers family? 

4. What was the average cost per mile for one person? 

6. Which islands of the West Indies did they visit? 



252 


THE BAYNE-SYLVESTER ARITHMETIC 


The Steamer 

The family stayed one night in San Juan and then took 
the steamer for New York. 

1. At the end of the first day out, the ship’s log read 
369 knots; the second day, 358.7 knots; the third day, 
371.2 knots; and the fourth day, 378.3 knots. What 
was the total distance in knots, or nautical miles? 

2. A knot is equivalent to 1.15 statute miles. What 
was the distance in statute miles? 

3. What was the average mileage per day? (Statute 
miles.) 

4. At $100 a person, what was the cost for steamer 
tickets? 

5. How far did the Rogers family travel from the time 
they left New York until they returned? 

6. How many days were they in making the trip? 

7. What was the average mileage per day for the entire 
trip? 


170. Commuting 

Walter’s family lives in Yonkers, but his father goes 
back and forth to New York each day to business. He 
travels on the railroad and uses a commutation ticket. 
This is a special ticket issued at a reduced rate. 

Most other persons who live out of town and go to 
town frequently, but not daily, buy a 50-Trip Family 
Ticket. This also is issued at a reduced rate. It is good 
for one year and can be used by any member of the family. 

The following is a schedule of rates between smaller 
cities and towns and the main railroad terminals in New 
York. 


SEVENTH GRADE 


253 


Single Ticket 

Commutation 

50-Trip 

Floral Park 

$.62 

$9.68 

$19.91 

Flushing 

$.34 

$7.81 

$9.63 

Garden City S.72 

$10.56 

$23.82 

Corona 

$.27 

$6.16 

$7.87 

Jamaica 

$.40 

$8.80 

$12.10 

Yonkers 

$.53 

$7.43 

$13.20 

Glenwood 

$.57 

$7.65 

$13.75 

Hastings 

$.69 

$8.31 

$16.72 

Dobbs Ferry $.72 

$8.47 

$17.60 

Irvington 

$.80 

$8.75 

$19.36 

1 . Mrs. 

Wilson lives 

in Floral Park. 

She made 50 


trips to the city during the first three months of the year. 
(a) How much would she have saved if she had bought a 
50-trip ticket? (b) About what per cent would she have 
saved? 

2. Find the difference in cost between a 50-trip ticket 
and 50 single tickets to New York for persons living in 
(a) Garden City, (b) Jamaica, (c) Yonkers, (d) Irvington, 
(e) Dobbs Ferry. 

3. About what per cent is saved by buying the 50- 
trip ticket in each case? 

4. What is the difference in cost between a single 
ticket and the fare one way at the 50-trip rate between 
(a) Flushing and New York, (b) Corona and New York, 
(c) Glenwood and New York, and (d) Hastings and New 
York. 

6. About what per cent of the regular cost per trip in 
Problem 4 is saved by buying at the 50-trip rate? 

6. A person who goes to the city every day would 
make how many trips (a) in February? (b) In Septem¬ 
ber? (c) In December? 


254 


THE BAYNE-SYLVESTER ARITHMETIC 


7. Allowing 60 trips as the maximum number a com¬ 
muter would be likely to make in a month, what is the 
cost of his passage one way to New York (a) from Irv¬ 
ington? (6) from Garden City? (c) from Glenwood? 
(d) from Jamaica? 

8. A business man or woman would probably go to 
the city on at least 24 days of the month. How many 
trips would he make? 

*9. Using this last figure as a basis for working out the 
commutation cost per trip, make a table showing the 
comparative costs of single tickets at the three rates. 

*10. What per cent of the cost of a single ticket is the 
cost of a ticket bought at each of the other rates? For a 
half cent or more allow an extra cent. For a half per 
cent or more, allow an extra per cent. 

*11. Mrs. Wright failed to use up her 50-trip ticket 
before the year was out. Upon what would her loss 
depend? 

171. Reading a Time-Table 

Robert’s father lives in Mount Vernon. This shows a 
section of the time-table he uses. 


Mi. 

Stations 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

PM 

0 

Lv G. Celt. Term. 
















Lower Level 

5.05 

5.10 

5.13 

5.20 

5.24 

5.27 

5.30 

5.40 

5.41 

5.42 

5.47 

5.56 

5.56 

6.03 

5 

Lv 125th Street . 

5.15 

5.20 

5.23 

5.30 

5.34 




5.51 

5.52 


6.06 

6.06 

6.13 

5 

Lv 138th Street . 

5.17 

5.22 

5.25 






5 53 

5.54 




6.15 

7 

Lv Melrose . 



5.27 






5.56 


6.01 



6.17 

7 

Lv Morrisania. 


5.26 







5.57 





6 19 

8 

Lv Claremont Pk. 



5.2. 






5.59 





6.21 
















8 

Lv Tremont. 


5.29 


5.38 





6.02 


6.06 

6.14 


6.23 

9 

Lv 183d Street. 



5.33 






6! 04 




6^26 

9 

Lv Fordham . 


5.33 


5.41 







6.10 



6.28 

10 

Lv Botanical Garden.. 



5.38 

5.43 







6.12 



6^31 
















11 

Lv Williams Bridge.. . 


5.38 


5.46 





6.08 


6.15 



6.34 

12 

Lv Woodlawn. 



5.44 

5.49 





6.12 


6.18 



6.37 

13 

Lv Wakefield. 



5.46 

5.51 





6 15 


6 20 



6 39 

14 

Lv Mount Vernon. ... 

5'29 

5.'46 

5.48 

5.53 

5.49 


5.54 


6.18 

6.'07 

6.23 

6.26 


6^43 
























































SEVENTH GRADE 255 

1. How far is Mount Vernon from the Grand Central 
Terminal? 

2. What train can Robert’s father take that will get 
him to Mount Vernon at about 5.30? 

3. One night he missed the 5.30 train. Which of the 
later trains would get him to Mount Vernon soonest? 

4. List the trains that make no stop between 125th 
Street and Mount Vernon. 

5. These trains are called_trains. 

6. Which train stops at every station? 

7. This train is called a_train. 

8. What is the difference in time from the Grand 
Central to Mount Vernon between the 5.24 and the 6.03 
train? 

9. Why cannot Robert’s father take the 5.27 train? 

10. Which other trains can he not use? 

11. Kate’s sister gets off at the Williams Bridge Station. 
Which trains stop at this station? 

12. If she misses the 5.10 train, what is the next train 
she can take? 

172. Showing the Results of a Competition 

The boys and girls in a seventh-grade class are competing 
to see which group will improve most in arithmetic. They 
are using the group averages in monthly tests as a basis for 
comparison, and a bar graph similar to the one on the next 
page to show the results. 

The graph on the blackboard was much larger, being 
drawn to the scale of | in. for 2%. The bar showing the 
record of the boys was colored yellow, and the bar showing 
the record of the girls was colored green. 


256 


THE BAYNE-SYLVESTER ARITHMETIC 


1. Which group was higher the first month? The 
second month? The third month? 

2. What per cent did the boys make the first month? 
The second month? The third 
month? 

3. What per cent did the 

girls make the first month? 

The second month? The third 
month? 

4. WTiat was the gain in per 
cent for the boys? The girls? 

6. Which group improved 
most? 

6. In which month were 

First Second Third -l-irkrl? 

Month Month Month tUey 1160 i 

173. Vocabulary Test 

Complete the following statements: 

1. The answer in an addition example is called the 

2. The numbers that are added are called- 

3. The answer in a subtraction example is called the 

_or_ 

4. In the example 624 - 324, the number 624 is the- 

and the number 324 is the_ 

5. To solve the example 62 X 348, we use the process 

called_ 

6. The answer in a multiplication example is called 

the_ 

7. The number by which we divide is called the- 

and the number that is to be divided is called the- 

The answer is called the_ 




































SEVENTH GRADE 257 

8. When goods are sold for more than cost, the dealer 

sells at a_ 

9. WRen goods are sold for less than cost, the dealer 

sells at a_ 

10. The sign + is used to indicate_It is read 

11. The sign — is used to indicate_It is read 


12. The sign X is used to indicate_It is read 


13. The sign -i- is used to indicate_It is read 

14. There are two kinds of fractions, common and_ 

15. The terms of a fraction are the_and the_ 

16. In the fraction f, 5 is the_and 8 is the_ 

17. In the number 6|, 6 is called an_, | is called a 

_, and 6^ is called a_ 

18. Write a mixed decimal. 

19. When two or more fractions have the same de¬ 
nominator, we say they have a- 

20. In the number 6.25, the whole number and the 

decimal are separated by a_It is read_ 

21. A fraction whose numerator is greater than its 

denominator is called an_ 

22. Explain drawing to scale.’^ ‘ 

23. What is a graph? 

24. A.M. means _ m. means_ p.m. means 

25. Name the instrument that shows mileage on an 
automobile; on a bicycle. 

26. What is meant by average mileage? Average 
attendance? Average weight? 












258 


THE BAYNE-SYLVESTER ARITHMETIC 


27. What are the factors of a number? Illustrate. 

28. John said he had a balance in the bank. What 
did he mean? 

29. Why is an estimate not an exact measurement? 

30. Mary made a deposit in the bank. What does that 
mean? 

174. Recording Your Progress in Arithmetic 

You are to keep a record of your progress in arithmetic 
this term on a line graph. 

On the next few pages in this book you will find tests 
which are marked Test I, II, III, IV, V, VI, VII, VIII, 
IX, X. There are 16 examples in each test. Try a new 
test every few weeks. 

Each time a test is given, record on the graph the 
number you have right. On a larger graph your teacher 
will show the record of the class. Then you can compare 
your record with the class record. 

At the end of the term your record should be higher 
than at the beginning of the term. 

Things to Remember 

If you wish to improve your score, 

1. Read your examples carefully. 

2. Think before you write. 

3. Check your work. 

4. Correct all mistakes and do some extra work on 
similar examples. 


SEVENTH GRADE 


259 


176. Tests 

You should complete each of these tests in about 30 
minutes. Work quickly, but do not hurry. Accuracy is 
more important than speed. Check your answers. 

Test I 


1. From 27 f take J, 

2. f - 5 = 

3. Multiply: 62.46 

2.5 


4. Five-eighths plus three- 
eighths = 

6. 5 X I = 

6. Of what number is 25 
one-fifth? 

7. Principal $650 
Time 1 yr. 

Rate 6% 

Interest ? 

8 . Find the sum: 

8 ft. 4 in. 

6 ft. 7 in. 

4 ft. 1 in. 


9. 2400 X 6252 = 

10. 625 is ? per cent of 1250 

11. S68.16 ^ 32 = 

12. Find 18% of $6425. 

13. 8359 
6426 
9589 
2786 
4583 
2784 


14. 620,400 

- 15,670 


15. of $61.50 = 

16. Find the area of a 
rectangle that measures 
8.4 yd. by 4.2 yd. 






260 THE BAYNE-SYLVESTER ARITHMETIC 

Test II 


1. From 12 yd. 1 ft. take 
9 yd. 2 ft. 

2. .3 + .6 + .8+.5 + .8 = 

3. Find the difference be¬ 
tween 14.875 and 200. 


4. .4)3.628 

5. Find the product of 
8296 and .427. 

6. Principal $1800 
Rate 6% 

Time 3 yr. 

Interest ? 

8. From 1 take f. 

9. 1000 X .8648 = 

10. 54 is ? per cent of 100 


11. I X 45 = 

12. $180 is 60% of ? 

13. lOi ^ 3 = 

14. Cost $2800 
Rate of gain 12% 
Gain ? 

16. 6246 
3897 
8469 
7684 
8329 
6846 
4587 


16. Find the perimeter of a 
square that measures 
7.25 yd. on a side. 




SEVENTH GRADE 


261 


Test III 

1. 86.4 + 283 + .462 + 

49.02 + 6.7 = 


2. Subtrahend 27,476 

Minuend 58,000 
Remainder • ? 

3. Seven-eighths plus three- 
fourths = 

4. 18i ^ 2 = 

5. 25 is ? per cent of 125 

6. 9367 multiplied by 
900 = 

7. Multiplicand 2384 

Multiplier .875 
Product ? 

8 . 

9. 5-^ minus ^ = 

10. 36 X = 

11. Cost $1250 
Rate of Loss 12% 

Loss ? 


12. 37i% of ? is 360 

13. Find the sum: 

6 gal. 2 qt. 

3 gal. 1 qt. 

5 gal. 3 qt. 

14. 69,876 
24,508 
87,604 
59,837 
69,859 
46,849 

16. Find the interest on 
$24,000 for 6 months at 
6 %. 

16. Find the area of a 
rectangle that measures 
12i rd. by 9j rd. 





262 


THE BAYNE-SYLVESTER ARITHMETIC 


Test IV 


1. 62)31,126 

2. List price 1540 
Discount 8% 
Selling price ? 

3. 8624 

928.6 

58.753 

9.24 

684.01 


4. .5 minus .2835 = 

6. 5.692 X 436 = 

6. Divide .2 by 25. 

7. 16f plus 28j plus 18f = 

8. From 18y take 14f. 

9. 40 X I = 


10. What per cent of 200 is 

8 ? 

11. Of what number is 72 
eight-ninths? 

12. From 6 gal. 1 qt. 

Take 5 gal. 3 qt. 

13. Change 56 f to an im¬ 
proper fraction. 

14. Principal $12,000 
Time 9 mo. 

Rate 5% 

Amount ? 

15. 12 - f = 

16. Find the area of a tri¬ 
angle whose altitude is 
9.6 yd. and whose base 
is 12.8 yd. 





SEVENTH GRADE 


263 


Test V 


1. 86,245 

9,286 

75,826 

7,896 

5,687 

98,765 

2. Find the difference be¬ 
tween .9 and .0075. 

3. Multiply 275 by 6.4. 

4. How much money will 
$5000 earn in 1 year 
6 months at 4%? 

6. Add: 6 lb. 7 oz. 

9 lb. 8 oz. 

2 lb. 5 oz. 

6. 2000 X 246.3 = 

7. Find 87i% of 6896. 


8. 100 is ? per cent of 50 

9. .6489 ^ 21 = 

10. Add: 48i 

12f 

27 

11. Multiply 8 by 2T- 

12. Divide 42 by f. 

13. 45^ 

- 26 A 

14. 24 is 6% of ? 

15. 4.5 X1 mi. equals_ft. 

16. Find the area of a tri¬ 
angle that has a base of 
16.8 ft. and an altitude 
of 8.4 ft. 






264 THE BAYNE-SYLVESTER ARITHMETIC 

Test VI 


1. What amount must be 
paid after 60 days if I 
borrow $9000 at 4%? 

2. What is the volume of a 
rectangular solid 9 ft. 
long, 8 ft. wide, and 6 
ft. high? 

3. From 7 hr. 25 min. take 
4 hr. 45 min. 

4. 625 + 86.4 + 275.254 
+ 36.27 = 

5. 68.2 - 4.2875 = 

6. 60i 



9. Find .5% of 624. 

10. What per cent of 800 is 
100 ? 

11. 8% of ? = $24 

12. How many feet are 
there in .75 mi.? 

13. 976.4 X .485 = 

14. 86,954 
27,836 

9,878 

56,989 

7,586 

88,493 


15. 16i- ^ i = 


7. 2| X * = 

8. 897.6 ^ 1000 = 16. 835)264 




SEVENTH GRADE 


265 


Test VII 


1. 612,563 ^ 76 = 

2. Multiply 70.86 by 67.8. 

3. Find i% of $1200. 

4. .66f of ? = 1500 

5. What interest is due on 
$8500 for 60 days at 
4%? 

6. Find the number of 
cubic inches in 2.5 cu.ft. 

7. Find the cubical con¬ 
tents of a rectangular 
solid 8j ft. by 6j ft. by 
8 ft. 

8 . 68.2 

4.275 

926. 

87.45 

3.9875 

60.05 


9. What is the difference 
between 18.006 and .24? 

10. .6298 -- 268 = 

11. Amount of Sale $540 

Commission 8% 

Net Proceeds ? 

12 . 200 | 

16 i 

27| 

26 i 


13. Minuend 28 f 
Subtrahend 4| 
Difference ? 

14. Divide 14| by f. 

15. 2i X 6i X I = 

16. Arrange the following 
in order of value and 
find the sum: .624, 6.24, 
62.4, .0624, 624. 




266 


THE BAYNE-SYLVESTER ARITHMETIC 


Test 

1. 87| plus 52^ plus 36f = 

2. Multiplicand 42 

Multiplier 
Product ? 

3. Subtract .29 from .6826. 


4. 9.6)864 

6. Find the product of 
8764 and 8.55. 

6. 9J 

- 8 | 

7. 4i X 13J X I = 

8 . ^ = 

9. Find 125% of 11600. 


VIII 

10. What per cent of 56 is 
35? 

11. What amount is due at 
the end of a year if the 
interest on $1500 at 4% 
is compounded quarter¬ 
ly? 

12. Change 26 sq. yd. 7 sq. 
ft. to square feet. 

13. Multiply 260 by 46f. 

14. Divide 10| by 5j. 

16. 905,463 9 = 

16. Find the area of a 
square that measures 
121 yd. on a side. 




SEVENTH GRADE 


267 


Test IX 


1. 476 minus .826 = 

2. 86,245 

9,378 

69,546 

8,620 

978 

79,876 


3. Multiply: 2800.6 
8.05 


4. Divide 364 by 3.25. 

6. 18f 

1 4 
1 5 

26f 

75 

6. Find the area of a 
rectangle that measures 
16i yd. by 32j yd. 

7. Find the difference be¬ 
tween 26 f and 25 f. 


8. Multiply 270f by 15. 

9. Rewrite the following 
numbers in order of 
value and find the sum: 
920, 9.2, .92, .092, 92. 

10. What is 2.5% of 500? 

11. $1200 is 125% of what 
number? 

12. How many cubic inches 
are there in .75 cu. ft.? 

13. Find the amount due 
on $1600 at the end of 
1 year when interest at 
3% is compounded 
quarterly. 

14. Find the cubical con¬ 
tents of a bin 8.4 yd. by 
6.2 yd. by 3.5 yd. 

16. 13A = 

16. 27 is ? per cent of 108 




268 


THE BAYNE-SYLVESTER ARITHMETIC 


Test X 


1. 826.4 + .275 + 826 
+ 46.375 + 29.2 = 

2. 43 f 
16f 

75 

3. Ill - = 

4 . 8 ) 56 ; 4 %^ 

5. Find 1% of $2400. 

6. 862.46 - 2.5583 = 

7. 36-^^ minus 24f = 

8. What per cent of 80 is 
50? 

9. Of what number is $950 
five-sevenths? 


10. .36)5473 

11. f X 2 y = 

12. Find the amount due 
on $15,000, borrowed 
for 90 days at 6%. 

13. 45.96 multiplied by 
2400 = 

14. Find the volume of a 
rectangular solid meas¬ 
uring 3j ft. by 2f ft. by 
4i ft. 

15. Find the area of a tri¬ 
angle having a base of 
53.2 yd. and an altitude 
of 26.5 yd. 

16. How many cubic yards 
are there in 21.6 cu. ft.? 




SEVENTH GRADE 


269 


176. Tables of Measure 

Linear Measure 

12 inches (in.) = 1 foot (ft.) 

3 feet = 1 yard (yd.) 
yards or 16j ft. = 1 rod (rd.) 

320 rods or 5280 ft. = 1 mile (mi.) 

Square Measure 

144 square inches (sq. in.) = 1 square foot (sq. ft.) 

9 square feet = 1 square yard (sq. yd.) 
30J square yards = 1 square rod (sq. rd.) 
160 square rods.= 1 acre (A.) 

640 acres = 1 square mile (sq. mi.) 

Measures of Volume 

1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 

27 cubic feet = 1 cubic yard (cu. yd.) 
128 cubic feet = 1 cord 

Measures of Weight 

16 ounces (oz.) = 1 pound (lb.) 

100 pounds = 1 hundredweight (cwt.) 

2000 pounds = 1 ton (T.) 

Liquid Measure 

4 gills (gi.) = 1 pint (pt.) 

2 pints = 1 quart (qt.) 

4 quarts = 1 gallon (gal.) 


270 


THE BAYNE-SYLVESTER ARITHMETIC 


Dry Measure 

2 pints (pt.) = 1 quart (qt.) 

8 quarts = 1 peck (pk.) 

4 pecks = 1 bushel (bu.) 

Table of Time 

60 seconds (sec.) = 1 minute (min.) 
60 minutes = 1 hour (hr.) 

24 hours = 1 day (da.) 

7 days = 1 week (wk.) 

30 days = 1 month (mo.) 

365 days = 1 year (yr.) 

366 days = 1 leap year 

Table of Number 

12 units = 1 dozen (doz.) 

12 dozen = 1 gross (gr.) 

12 gross = 1 great gross 
20 units = 1 score 

United States Money 

10 mills = 1 cent (f) 

10 cents = 1 dime 
10 dimes = 1 dollar ($) 


SEVENTH GRADE 


271 


Equivalents 


1 gallon of water 
1 gallon 
1 cubic foot of water 
1 cubic foot 
1 bushel 
1 bushel of wheat 
1 bushel of corn 
1 bushel of oats 
1 load of earth 
1760 yards 
1 hand 
1 fathom 
1 knot 
1 section 
1 square 
1 hogshead 


8^ pounds 
231 cubic inches 
62j pounds 
7J gallons 
Ij cubic feet 
60 pounds 
56 pounds 
32 pounds 
1 cubic yard 
1 mile 
4 inches 
6 feet 

1.15 miles (nearly) 
1 square mile 
100 square feet 
63 gallons 







INDEX 


Addition 
Decimals, 26 
Fractions, 8, 9 
Harder combinations, 27 
Integers, 26 
See also Test Drills 
Areas 

Rectangles, 161 
Right triangles, 163 

Banks, 204 
Checks, 115, 206 
Deposit slips, 205 
Keeping an account, 210 
Bills, 109 

Buying by the Hundred and the 
Thousand, 44 

Checks, 115, 206 
Commission, 125 

Finding commission, 126 
Finding the net proceeds, 127 
Problems, 216 
Review of terms, 130 
Completion Exercise, 68 
Sentences for, 70, 231 
Contents of Rectangular Solids, 241 

Decimals 
Addition, 26 
Division, 42 

Selecting the correct quotient, 
47 

Finding a decimal part, 75 
Finding a number when a deci¬ 
mal part is given, 78 
Finding what decimal part one 
number is of another, 76 
Multiplication, 36 
Placing decimal point, 39 
Practice with, 50 
Reading and writing, 3 
Subtraction, 30 


What you should know about 
decimals, 51 
See also Test Drills 
Denominate Numbers, see Measure¬ 
ments 
Discount 

Discount sales, 187 
Net cost, 188 
Review of terms, 193 
Short way of finding net cost, 129 
Trade, 188 
Division 
Decimals, 42, 47 
Difficult combinations, 45 
Fractions, 18, 19 
Integers, 42 
See also Test Drills 

Estimating, 72 

Fractions 

Addition, 8, 9 
Division 18, 19 
Finding a fractional part, 75 
Finding a number when a frac¬ 
tional part is given, 78 
Finding what fraction one num¬ 
ber is of another, 76 
Multiplication, 15, 16 
Principles, 21 
Problems, 23, 25 
Reduction of, 6 
Reviev/ of common, 71 
Subtraction, 12, 13 
See also Test Drills 

Graphs 
Bar, 166 

Line, to show comparison, 231, 
256 

Interest, 211 
Record of’progress, 164 


273 



274 


INDEX 


Interest, 131 
Compound, 201, 214 
Finding from graph, 210 
Formula, 138, 200 
Problems, 137, 199, 203, 213 
Simple 
Days, 194 
Less than year, 134 
More than one year, 132 
Year, 132 

Years and months, 135 
Review, 193 
See also Test Drills 


Measurement 

Addition of denominate numbers, 
86 

Cubic, 245, 246 

Denominate number race, 170, 
248 

Division of denominate numbers, 
89 

Equivalents, 271 
Linear, 82 
Liquid, 81 

Multiplication of denominate 
numbers, 88 
Reduction, 79 
Square, 84 

Standard weights of a bushel, 169 
Subtraction of denominate num¬ 
bers, 87 
Tables, 269 
Time, 83 
Weight, 85, 269 
Meters, How to Read 
Electric, 92, 94 
Gas, 97 

Problems, 95, 99 
Miscellaneous Problems, 217 
Money 

Foreign, 224, 226 
United States, 270 
Multiplication 
Decimals, 36 

Difficult combinations, 38 
Fractions, 15, 16 
Integers, 36 
Problems, 40 
See also Test Drills 


Order Blanks, 105 

Parcel Post, 157 
Percentage, 52 

Adding and subtracting, 56 
Estimating per cents, 72 
Finding a number when a per 
cent is given, 64 

Finding a per cent of a number, 
53 

Finding what per cent one num¬ 
ber is of another, 61 
Per cents less than 1, 69 
Per cents more than 100, 57 
Problems, 63, 66, 77, 214 
Race, 73 
Review, 72 

Short ways of finding per cent, 59 
See also Test Drills 
Postal Money Orders, 160, 161 
Problems about 

Airplane travel, 155 
Ball team, 151 
Commuting, 252 
Geography, 33 
Holiday in South, 249 
Home, 182 
Household, 90 
Paying for electricity, 92 
Paying for gas, 97 
Rainfall, 49 

Time-tables, 152, 153, 155, 254 
Using a ticket schedule, 156 
Problem Study 
Analysis, 142, 232 
Approximating answers, 145, 235 
Changing the wording, 147, 237 
Selecting the operation, 146, 236 
Silent reading, 149, 239 
Supplying the question, 144, 234 
Without numbers, 148, 238 
Profit and Loss, 115, 118 
Finding the cost, 124 
Finding the per cent of profit or 
loss, 120 

Finding the selling price, 119 
Review, 122 

Reading and Writing Numbers, 1, 3 
Reading Meters, 94, 97 
Receipts, 112 



INDEX 


275 


Recording Progress, 171, 258 
Rectangles, 161 
Right Angles, 161, 163 
Roman Numbers, 5 

Sales Slips, 106 
Subtraction 
Decimals, 30 
Fractions, 12, 13 
Integers, 30 
See also Test Drills 

Taxes, 227, 229, 230 
Test Drills 
Addition 
Decimals, 29 
Fractions, 11 
Integers, 28 
Division 

Decimals, 48 
Fractions, 20 


How to use, 10 
Multiplication 
Decimals, 41 
Fractions, 17 
Percentage, 74 
Applications, 140, 220 
Interest, 141, 221 
Subtraction 
Decimals, 32 
Fractions, 14 
Integers, 31 
Tests 

Achievement 
7 A — 172-181 
7 B — 259-267 
Same — Different, 222 
Vocabulary, 256 
Thrift, 100, 102, 186 


Volume, 241 



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